Gr 12 Mathematics: Ch 9 Sum Probability

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What is the probability of the union of two mutually exclusive events A and B?

P(A) + P(B) (correct)

P(A) / P(B)

P(A) - P(B)

P(A) × P(B)

What is the complementary rule in probability?

P(not A) = P(A) + 1

P(not A) = 1 - P(A) (correct)

P(not A) = P(A)

P(not A) = P(A) - 1

What is the purpose of a Venn diagram in probability?

To show the probability of an event

To visualize the relationships between events (correct)

To simplify complex probability problems

To calculate the probability of an event

What is the product rule for independent events?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the definition of mutually exclusive events?

Events that cannot occur simultaneously Signup and view all the answers

What is the symbol for the sample space in probability?

S Signup and view all the answers

What is the purpose of a tree diagram in probability?

To organize and visualize the different possible outcomes of a sequence of events Signup and view all the answers

What is the definition of complementary events?

Events that are mutually exclusive and make up the whole sample space Signup and view all the answers

What is the formula for the probability of the intersection of two events A and B?

P(A) × P(B) Signup and view all the answers

What is the purpose of a two-way contingency table in probability?

To organize and record the counts or percentages in a probability problem Signup and view all the answers

What is the addition rule for any two events A and B?

P(A or B) = P(A) + P(B) - P(A and B) Signup and view all the answers

What is the simplification of the addition rule for two mutually exclusive events?

P(A or B) = P(A) + P(B) Signup and view all the answers

What is the complementary rule?

P(not A) = 1 - P(A) Signup and view all the answers

What is the product rule for independent events?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the condition for two events to be mutually exclusive?

P(A and B) = 0 Signup and view all the answers

What is the condition for two events to be independent?

P(A and B) = P(A) × P(B) Signup and view all the answers

Why is it incorrect to assume that mutually exclusive events are independent?

Because mutually exclusive events do not satisfy the product rule. Signup and view all the answers

What should you verify to test whether events are independent?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

P(A) × P(B) Signup and view all the answers

What is the formula for the total number of outcomes in two events A and B, where there are n(A) outcomes in event A and n(B) outcomes in event B?

n(A) × n(B) Signup and view all the answers

What is the definition of A' in probability theory?

The complement of set A Signup and view all the answers

What is the formula for the total number of arrangements of n different objects?

n! Signup and view all the answers

What is the definition of n! (read as 'n factorial')?

The product of all positive integers up to n Signup and view all the answers

What is the formula for calculating the probability of an event A not occurring?

1 - P(A) Signup and view all the answers

What is the formula for the total number of outcomes when there are n objects to choose from and you choose from them r times?

n^r Signup and view all the answers

What is the formula for the probability of two mutually exclusive events A and B occurring?

P(A) + P(B) Signup and view all the answers

What is the value of 0! (zero factorial)?

1 Signup and view all the answers

What is the purpose of the Fundamental Counting Principle?

To count the number of outcomes in multiple events Signup and view all the answers

What is the value of 0!?"

1 Signup and view all the answers

What is the number of ways to arrange 5 different objects?

120 Signup and view all the answers

If 8 athletes participate in a 400 m race, how many ways can the first three places be arranged?

336 Signup and view all the answers

What is the formula to find the total number of arrangements of 7 distinct objects?

7! Signup and view all the answers

How many arrangements are possible for the letters in the word 'BASSOON'?

2520 Signup and view all the answers

What is the probability of an event when there are 10 favorable outcomes and 100 total outcomes?

1/10 Signup and view all the answers

What is the number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

10000 Signup and view all the answers

What is the formula to find the total number of arrangements of n distinct objects?

n! Signup and view all the answers

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

Property 1 Signup and view all the answers

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

as a single entity Signup and view all the answers

What is the total number of possible PINs if digits cannot be repeated?

5,040 Signup and view all the answers

What is the probability of a PIN containing at least one 8 if digits can be repeated?

0.3439 Signup and view all the answers

What is the number of possible number plates consisting of 3 letters followed by 3 digits?

926,100 Signup and view all the answers

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

0.216 Signup and view all the answers

What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are treated as identical?

1,260 Signup and view all the answers

What is the number of arrangements of the word 'BASSOON' starting and ending with the same letter?

120 Signup and view all the answers

What is the probability that the word 'BASSOON' starts and ends with the same letter?

0.0952 Signup and view all the answers

What is the total number of possible PINs if digits can be repeated?

10,000 Signup and view all the answers

What is the purpose of the addition rule in probability?

To find the probability of the union of two events Signup and view all the answers

What is the condition for two events to be independent?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the formula for the probability of the complement of an event A?

1 - P(A) Signup and view all the answers

What is true about mutually exclusive events?

P(A and B) = 0 Signup and view all the answers

What is the difference between mutually exclusive and independent events?

Mutually exclusive means P(A and B) = 0, while independent means P(A and B) = P(A) × P(B) Signup and view all the answers

When can the addition rule be simplified to P(A or B) = P(A) + P(B)?

When A and B are mutually exclusive Signup and view all the answers

What is the formula for the probability of the intersection of two independent events A and B?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the relationship between the probability of an event and its complement?

P(A) + P(A') = 1 Signup and view all the answers

What is the condition for two events to be mutually exclusive?

The events must not have any common outcomes. Signup and view all the answers

What is the formula for the probability of the union of two mutually exclusive events A and B?

P(A) + P(B) Signup and view all the answers

What is represented by the region outside the shape in a Venn diagram?

The outcomes not in the event Signup and view all the answers

What is the probability of an event A not occurring, given P(A) = 0.6?

0.4 Signup and view all the answers

What is the purpose of a two-way contingency table?

To show the relationship between two events Signup and view all the answers

What is the symbol for the sample space?

S Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

P(A) × P(B) Signup and view all the answers

What is the condition for two events to be complementary?

The events must be mutually exclusive and make up the whole sample space. Signup and view all the answers

What is the purpose of a tree diagram?

To organize and visualize the different possible outcomes of a sequence of events Signup and view all the answers

What is the probability of event A, given P(not A) = 0.3?

0.7 Signup and view all the answers

What is the formula for the probability of event A not occurring?

1 - P(A) Signup and view all the answers

What is the total number of outcomes when there are n objects to choose from and you choose from them r times, with repetition allowed?

n × n × ... (r times) Signup and view all the answers

What is the formula for the total number of arrangements of n different objects?

n × (n - 1) × ... × 1 Signup and view all the answers

What is the purpose of the fundamental counting principle?

To count the number of outcomes in multiple events Signup and view all the answers

What is the condition for two events to be independent?

The occurrence of one event does not affect the probability of the other event Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

P(A) × P(B) Signup and view all the answers

What is the formula for the total number of outcomes in two events A and B, where there are n(A) outcomes in event A and n(B) outcomes in event B?

n(A) × n(B) Signup and view all the answers

What is the definition of n! (read as 'n factorial')?

The product of all positive integers up to n Signup and view all the answers

What is the total number of possible arrangements of 7 distinct objects?

7 × 6 × 5 × 4 × 3 × 2 × 1 Signup and view all the answers

What is the value of 0! (zero factorial)?

1 Signup and view all the answers

What is the total number of possible arrangements of 5 different objects?

5! Signup and view all the answers

What is the total number of ways to arrange the first three places in a 400 m race with 8 athletes?

336 Signup and view all the answers

What is the total number of arrangements of the letters in the word 'BASSOON'?

7! / (2! × 2!) Signup and view all the answers

What is the probability of an event when there are 20 favourable outcomes and 100 total outcomes?

20/100 Signup and view all the answers

What is the total number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

10^4 Signup and view all the answers

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

n! = the product of all positive integers less than or equal to n Signup and view all the answers

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

As a single entity Signup and view all the answers

What is the total number of arrangements of the letters in the word 'BASSOON' if repeated letters are treated as identical?

7! / (2! × 2!) Signup and view all the answers

What is the probability of an event when there are 10 favourable outcomes and 50 total outcomes?

10/50 Signup and view all the answers

What is the formula for the probability of an event E?

P(E) = n(E) / n(S) Signup and view all the answers

If a PIN consists of 4 digits (0-9) with no repetition, what is the total number of possible PINs?

5040 Signup and view all the answers

What is the probability of a PIN containing at least one 8 if digits can be repeated?

0.3439 Signup and view all the answers

If a number plate consists of 3 letters (excluding vowels and 'Q') followed by 3 digits (0-9), what is the total number of possible number plates?

926100 Signup and view all the answers

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

0.216 Signup and view all the answers

For the word 'BASSOON', what is the total number of possible arrangements if repeated letters are treated as identical?

1260 Signup and view all the answers

What is the probability that the word 'BASSOON' starts and ends with the same letter?

0.0952 Signup and view all the answers

If a PIN consists of 4 digits (0-9) with repetition, what is the total number of possible PINs?

10000 Signup and view all the answers

What is the number of PINs with no 8's if digits can be repeated?

6561 Signup and view all the answers

If P(A) = 0.3 and P(B) = 0.5, what is P(A or B) if A and B are independent?

0.65 Signup and view all the answers

If P(A and B) = 0.2 and P(A) = 0.4, what is P(B) if A and B are independent?

0.5 Signup and view all the answers

What is P(not A) if P(A) = 0.7?

0.3 Signup and view all the answers

If P(A) = 0.2 and P(B) = 0.6, what is P(A and B) if A and B are mutually exclusive?

0 Signup and view all the answers

What is the relationship between P(A) and P(not A)?

P(A) + P(not A) = 1 Signup and view all the answers

If P(A or B) = 0.8 and P(A and B) = 0.2, what is P(A)?

0.6 Signup and view all the answers

What is true about mutually exclusive and independent events?

Mutual exclusivity and independence are distinct concepts Signup and view all the answers

If P(A) = 0.5 and P(B) = 0.3, what is P(A or B) if A and B are dependent?

Cannot be determined Signup and view all the answers

What is the condition for two events to be mutually exclusive?

P(A and B) = 0 Signup and view all the answers

What is the purpose of a two-way contingency table?

To keep a record of the counts or percentages in a probability problem Signup and view all the answers

What is the formula for the probability of the complement of an event A?

P(A') = 1 - P(A) Signup and view all the answers

What is the symbol for the sample space in probability?

S Signup and view all the answers

What is true about complementary events?

They are mutually exclusive and make up the whole sample space Signup and view all the answers

What is the purpose of a Venn diagram in probability?

To visualize the relationship between events Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the condition for two events to be independent?

P(A and B) = P(A) × P(B) Signup and view all the answers

What is the formula for the union of two events A and B?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Signup and view all the answers

What is the purpose of the product rule in probability?

To calculate the probability of the intersection of two events Signup and view all the answers

What is the probability of a PIN containing at least one 8 if digits cannot be repeated?

0.4 Signup and view all the answers

What is the total number of possible number plates consisting of 3 letters followed by 3 digits?

926,100 Signup and view all the answers

What is the number of arrangements of the word 'BASSOON' starting and ending with the same letter?

120 Signup and view all the answers

What is the probability that a PIN contains at least one 8 if digits can be repeated?

0.3439 Signup and view all the answers

If two events A and B are independent, which of the following is true?

P(A ∩ B) = P(A) × P(B) Signup and view all the answers

What is the total number of possible PINs if digits cannot be repeated?

5,040 Signup and view all the answers

If A and B are two events such that A ⊆ B, then which of the following is true?

P(A) ≤ P(B) Signup and view all the answers

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

0.216 Signup and view all the answers

If there are 5 different objects, how many ways are there to arrange them?

5! Signup and view all the answers

What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are treated as identical?

1,260 Signup and view all the answers

What is the probability that the word 'BASSOON' starts and ends with the same letter?

0.0952 Signup and view all the answers

If A and B are two mutually exclusive events, then which of the following is true?

P(A ∩ B) = 0 Signup and view all the answers

If there are 10 objects to choose from and you choose from them 3 times, how many possible outcomes are there?

10^3 Signup and view all the answers

If A is an event, what is the probability of not A?

P(A') = 1 - P(A) Signup and view all the answers

If there are 5 different objects, how many ways are there to arrange 3 of them?

5 × 4 × 3 Signup and view all the answers

What is the formula for the probability of the union of two events A and B?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Signup and view all the answers

What is the value of 0!?

1 Signup and view all the answers

If there are 5 different objects, how many ways are there to arrange them in a circle?

(5 - 1)! Signup and view all the answers

What is the total number of ways to arrange the letters in the word 'BASSOON' if the repeated letters are treated as identical?

630 Signup and view all the answers

If seven boys are sitting in a row, and the youngest and oldest must not sit together, what is the total number of arrangements?

3600 Signup and view all the answers

What is the total number of ways to arrange the first three places in a 400m race with 8 athletes?

336 Signup and view all the answers

What is the formula to find the total number of arrangements of n distinct objects?

$n imes (n - 1) imes (n - 2) imes \cdots imes 3 imes 2 imes 1$ Signup and view all the answers

What is the probability of a random arrangement of letters starting and ending with a specific letter?

1/8 Signup and view all the answers

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

As one entity Signup and view all the answers

What is the total number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

10000 Signup and view all the answers

What is the formula to find the probability of an event E?

$P(E) = rac{n(E)}{n(S)}$ Signup and view all the answers

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

The first property of factorial notation Signup and view all the answers

What is the total number of ways to arrange the letters in the word 'BASSOON' if repeated letters are treated as different?

5040 Signup and view all the answers

If two events A and B are independent, what is the value of P(A and B) - P(A)P(B)?

0 Signup and view all the answers

What is the probability of the union of two events A and B, given that P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.2?

0.7 Signup and view all the answers

If P(A) = 0.6 and P(not A) = 0.4, what is the value of P(A or not A)?

1 Signup and view all the answers

What is the probability of the intersection of two events A and B, given that P(A) = 0.5, P(B) = 0.7, and they are independent?

0.35 Signup and view all the answers

If two events A and B are mutually exclusive, what is the value of P(A and B)?

0 Signup and view all the answers

What is the purpose of the complementary rule in probability?

To find the probability of the complement of an event Signup and view all the answers

If two events A and B are independent, what is the value of P(A) - P(A and B)?

0 Signup and view all the answers

What is the relationship between mutually exclusive and independent events?

Mutually exclusive and independent are distinct concepts Signup and view all the answers

Which of the following is true about mutually exclusive events?

They never occur simultaneously and have an empty intersection. Signup and view all the answers

What is the purpose of a tree diagram in probability?

To organize and visualize the different possible outcomes of a sequence of events. Signup and view all the answers

If two events A and B are dependent, then:

P(A and B) ≠ P(A) × P(B). Signup and view all the answers

What is the formula for the probability of the complement of an event A?

P(not A) = 1 - P(A). Signup and view all the answers

What is the purpose of a two-way contingency table in probability?

To keep a record of the counts or percentages in a probability problem. Signup and view all the answers

What is the symbol for the sample space in probability?

S. Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

P(A and B) = P(A) × P(B). Signup and view all the answers

What is the condition for two events to be mutually exclusive?

P(A and B) = 0. Signup and view all the answers

What is the purpose of Venn diagrams in probability?

To show how events are related to one another. Signup and view all the answers

What is true about the intersection of two mutually exclusive events?

It is always empty. Signup and view all the answers

If A and B are two events such that P(A) = 0.3 and P(B) = 0.4, and P(A and B) = 0.12, then what is P(A or B)?

0.64 Signup and view all the answers

If A and B are two independent events such that P(A) = 0.25 and P(B) = 0.5, then what is P(A and B)?

0.125 Signup and view all the answers

If a box contains 5 red balls, 3 blue balls, and 2 green balls, and a ball is drawn at random, what is the probability that it is not blue?

7/10 Signup and view all the answers

If 5 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with repetition allowed, what is the total number of possible outcomes?

10^5 Signup and view all the answers

If 3 letters are chosen from the set {A, B, C, D, E, F} without repetition, what is the total number of possible outcomes?

6P3 Signup and view all the answers

If A and B are two events such that P(A) = 0.6 and P(B) = 0.4, and P(A or B) = 0.8, then what is P(A and B)?

0.2 Signup and view all the answers

If a fair six-sided die is rolled 4 times, what is the total number of possible outcomes?

6^4 Signup and view all the answers

If 7 different books are arranged on a shelf, what is the total number of possible arrangements?

7! Signup and view all the answers

If A and B are two independent events such that P(A) = 0.4 and P(B) = 0.3, then what is P(not A and not B)?

0.58 Signup and view all the answers

If a committee of 4 people is chosen from a group of 10 people, what is the total number of possible committees?

10C4 Signup and view all the answers

If the digits in a PIN cannot be repeated, what is the probability that the PIN contains at least one 8?

0.4 Signup and view all the answers

What is the total number of possible number plates consisting of 3 letters (excluding vowels and 'Q') followed by 3 digits (0-9)?

926,100 Signup and view all the answers

For the word 'BASSOON', what is the probability that the word starts and ends with the same letter?

0.0952 Signup and view all the answers

What is the total number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

10,000 Signup and view all the answers

If the digits in a PIN can be repeated, what is the probability that the PIN contains at least one 8?

0.3439 Signup and view all the answers

What is the probability that a number plate starts with 'Y' and ends with an odd digit?

0.216 Signup and view all the answers

For the word 'BASSOON', what is the total number of possible arrangements if repeated letters are treated as identical?

1,260 Signup and view all the answers

If the digits in a PIN cannot be repeated, what is the total number of possible PINs?

5,040 Signup and view all the answers

How many ways can the letters in the word 'STATISTIC' be arranged?

10! / (2! × 2! × 1! × 1!) Signup and view all the answers

What is the total number of possible arrangements of 9 distinct objects?

9! Signup and view all the answers

A password consists of 6 characters, where each character can be any of the 26 lowercase English letters. How many possible passwords are there?

26^6 Signup and view all the answers

What is the total number of possible arrangements of 5 distinct objects, where one object is fixed in one position?

4! Signup and view all the answers

What is the total number of possible arrangements of the letters in the word 'MISSISSIPPI'?

11! / (4! × 4! × 2!) Signup and view all the answers

How many ways can 8 athletes be arranged in a 400 m race?

8! Signup and view all the answers

What is the total number of possible arrangements of the letters in the word 'BANANA'?

6! / (3! × 2!) Signup and view all the answers

What is the total number of possible arrangements of the letters in the word 'ORANGE'?

6! / (2! × 1!) Signup and view all the answers

What is the total number of possible arrangements of 7 distinct objects, where the youngest and oldest objects must sit together?

6! × 2! Signup and view all the answers

Gr 12 Mathematics: Ch 9 Sum Probability

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Questions and Answers

What is the probability of the union of two mutually exclusive events A and B?

What is the complementary rule in probability?

What is the purpose of a Venn diagram in probability?

What is the product rule for independent events?

What is the definition of mutually exclusive events?

What is the symbol for the sample space in probability?

What is the purpose of a tree diagram in probability?

What is the definition of complementary events?

What is the formula for the probability of the intersection of two events A and B?

What is the purpose of a two-way contingency table in probability?

What is the addition rule for any two events A and B?

What is the simplification of the addition rule for two mutually exclusive events?

What is the complementary rule?

What is the product rule for independent events?

What is the condition for two events to be mutually exclusive?

What is the condition for two events to be independent?

Why is it incorrect to assume that mutually exclusive events are independent?

What should you verify to test whether events are independent?

What is the formula for the probability of two independent events A and B occurring?

What is the formula for the total number of outcomes in two events A and B, where there are n(A) outcomes in event A and n(B) outcomes in event B?

What is the definition of A' in probability theory?

What is the formula for the total number of arrangements of n different objects?

What is the definition of n! (read as 'n factorial')?

What is the formula for calculating the probability of an event A not occurring?

What is the formula for the total number of outcomes when there are n objects to choose from and you choose from them r times?

What is the formula for the probability of two mutually exclusive events A and B occurring?

What is the value of 0! (zero factorial)?

What is the purpose of the Fundamental Counting Principle?

What is the value of 0!?"

What is the number of ways to arrange 5 different objects?

If 8 athletes participate in a 400 m race, how many ways can the first three places be arranged?

What is the formula to find the total number of arrangements of 7 distinct objects?

How many arrangements are possible for the letters in the word 'BASSOON'?

What is the probability of an event when there are 10 favorable outcomes and 100 total outcomes?

What is the number of possible PINs if each of the four digits can be any of the 10 digits (0-9)?

What is the formula to find the total number of arrangements of n distinct objects?

What is the property of factorial notation that states the factorial of any non-negative integer n is the product of all positive integers less than or equal to n?

If the constraint in an arrangement problem is that the youngest and oldest must sit together, how do you treat this pair?

What is the total number of possible PINs if digits cannot be repeated?

What is the probability of a PIN containing at least one 8 if digits can be repeated?

What is the number of possible number plates consisting of 3 letters followed by 3 digits?

What is the probability that the number plate starts with 'Y' and ends with an odd digit?

What is the total number of possible arrangements of the word 'BASSOON' if repeated letters are treated as identical?

What is the number of arrangements of the word 'BASSOON' starting and ending with the same letter?

What is the probability that the word 'BASSOON' starts and ends with the same letter?

What is the total number of possible PINs if digits can be repeated?

What is the purpose of the addition rule in probability?

What is the condition for two events to be independent?

What is the formula for the probability of the complement of an event A?

What is true about mutually exclusive events?

What is the difference between mutually exclusive and independent events?

When can the addition rule be simplified to P(A or B) = P(A) + P(B)?

What is the formula for the probability of the intersection of two independent events A and B?

What is the relationship between the probability of an event and its complement?

What is the condition for two events to be mutually exclusive?

What is the formula for the probability of the union of two mutually exclusive events A and B?

What is represented by the region outside the shape in a Venn diagram?

What is the probability of an event A not occurring, given P(A) = 0.6?

What is the purpose of a two-way contingency table?

What is the symbol for the sample space?

What is the formula for the probability of two independent events A and B occurring?

What is the condition for two events to be complementary?

What is the purpose of a tree diagram?

What is the probability of event A, given P(not A) = 0.3?

What is the formula for the probability of event A not occurring?

What is the total number of outcomes when there are n objects to choose from and you choose from them r times, with repetition allowed?

What is the formula for the total number of arrangements of n different objects?

What is the purpose of the fundamental counting principle?

What is the condition for two events to be independent?

What is the formula for the probability of two independent events A and B occurring?

What is the formula for the total number of outcomes in two events A and B, where there are n(A) outcomes in event A and n(B) outcomes in event B?

What is the definition of n! (read as 'n factorial')?

What is the total number of possible arrangements of 7 distinct objects?

What is the value of 0! (zero factorial)?

What is the total number of possible arrangements of 5 different objects?

What is the total number of ways to arrange the first three places in a 400 m race with 8 athletes?