Fundamental Counting Principle and Permutations

In a scenario with limited possible outcomes, what visual tool is most effective for determining all possibilities?

How many different outfits can be made from 4 shirts and 3 pairs of pants?

What is a permutation?

In how many ways can a president, a secretary, and a treasurer be chosen from a group of 10 people?

Given the expression $\frac{7!}{5!}$, what is its simplified value?

How many different four-letter words can be formed from the letters of the word RAINBOW, assuming each letter is used only once?

Simplify the following expression: $\frac{(n+2)!}{n!}$

What is the value of 1! + 0!?

A restaurant offers 4 appetizers, 6 main courses, and 3 desserts. If a customer wants to order one item from each category, how many different meal combinations are possible?

A password must be 6 characters long. The characters can be either upper-case letters (A-Z) or digits (0-9). How many different passwords are possible if characters can be repeated?

A student is creating a schedule of classes. They must choose 1 of 3 math courses, 1 of 4 science courses, and 1 of 2 history courses. How many different schedules can be created?

A car manufacturer offers a car in 5 different colors, with 3 different engine options, and with or without a sunroof. How many different versions of the car can be manufactured?

A pizza shop allows customers to choose one crust from 3 options (thin, regular, deep-dish), one cheese from 4 options (cheddar, mozzarella, provolone, parmesan) and one topping from 5 options (pepperoni, sausage, mushrooms, olives, peppers). How many different pizzas can be ordered?

A website requires a user to create a PIN consisting of 4 digits. Digits can be repeated. If the first digit cannot be zero, then how many different PINs are possible?

How many different 3-letter codes can be formed from the letters of the word 'PROBLEM', if each letter can only be used once in each code?

Sarah wants to set up an aquarium. She has 7 choices for fish, 4 choices for plants, and 3 choices for substrate. If she decides she wants one of each in her aquarium, how many different aquariums can she create?

Which of the following best describes the relationship between an experiment, sample space, and event?

Given a sample space $U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ and an event $A = {2, 4, 6, 8}$, what is the complement of A (A')?

In probability, what distinguishes a simple event from a compound event?

Events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is the probability of either A or B occurring (P(A∪B))?

If two events are NOT mutually exclusive, what does this imply?

What is the significance of the sample space in probability?

A fair six-sided die is rolled. Event A is rolling an even number, and Event B is rolling a number greater than 4. What is P(A)?

Using the formula for probability, what does the numerator represent?

A jar contains 4 red, 6 green, 3 blue, and 7 yellow marbles. A marble is chosen randomly, and without replacing it, a second marble is chosen. What is the probability of choosing a red marble first and then a blue marble?

A box contains 5 white, 7 black, and 3 orange balls. Two balls are drawn without replacement. What is the probability that the first ball is white and the second is black?

In a class of 25 students, 10 are taking French, 8 are taking Spanish, and 3 are taking both. If a student is chosen at random, what is the probability they are only taking French?

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. Two marbles are drawn with replacement. What is the probability that both marbles are red?

There are 20 computers, 4 of which are defective. If three computers are chosen at random for testing, what is the probability that all three are defective if the computers are not replaced?

A box contains 50 light bulbs, 5 of which are defective. If two light bulbs are randomly selected without replacement, what is the probability that the both are defective?

A fair six-sided die is rolled twice. What is the probability of rolling an even number on the first roll and a number greater than 4 on the second roll?

In a shipment of 25 items, 5 are defective. If two items are chosen at random, what is the probability that neither is defective?

Given set A = {1, 2, 3, 4, 5, 6} and set B = {0, 2, 4, 6, 7}, what is the intersection of sets A and B (A Ç B)?

A coin is tossed three times. What represents the probability of getting either all heads or exactly one head?

What is the correct formula to calculate the probability of the union of two inclusive events A and B?

If event A is 'drawing a 3 from a set of numbers 1 to 6' and event B is 'drawing an even number from the same set', what is P(AUB)?

In probability, what distinguishes independent events from dependent events?

A number is selected from 1 to 15. Event A is 'divisible by 3' and event B is 'divisible by 4'. What is the probability of P(AÇB)?

Events A and B are independent. If P(A) = 0.6 and P(B) = 0.2, what is the probability of both A and B occurring?

A die is rolled. What is the probability of getting an even number OR a five?

What does AÇB represent in probability theory?

A bag contains 5 red balls and 3 blue balls. Two balls are drawn without replacement. What concept is important for calculating the probability of drawing a blue ball on the second draw, given that a red ball was drawn first?

In a scenario where event A influences event B, altering its probability, which formula accurately calculates the probability of both events A and B occurring?

A box contains 5 red balls and 3 blue balls. Two balls are drawn without replacement. What is the probability that the first ball is red and the second ball is blue?

A bag contains 4 white marbles and 6 black marbles. Two marbles are drawn in succession without replacement. What is the probability that both marbles are black?

From a standard deck of 52 cards, two cards are drawn without replacement. What is the probability that the first card is a King and the second card is a Queen?

In a class, 30% of students failed a math test and 20% failed both math and English tests. What percentage of students who failed the math test also failed the English test?

A box contains 7 apples and 3 oranges. If two fruits are picked at random without replacement, what is the probability that the first fruit is an apple and the second is an orange?

A jar contains 5 blue marbles and 4 red marbles. Two marbles are selected at random without replacement. What is the probability that the first marble is blue, and the second is also blue?

In a shipment of 15 items, 4 are defective. If two items are randomly selected without replacement, what is the probability that both items are defective?

Fundamental Counting Principle

Tree Diagram

Sample Space

Outfit Combinations

Event 1

Event 2

Outcomes Table

Combinatorial Maths

Complement of an Event

Experiment

Outcome

Sample Point

Union of Sets

Mutually Exclusive Events

Probability Formula

Permutation

nPr Notation

Factorial Notation

Combinations vs Permutations

Example of Permutation

Factorial of Zero

FCP (Fundamental Counting Principle)

Dependent Events

Probability of Dependent Events

Without Replacement

Defective Computers Probability

Multiple Variable Probability

Card Selection Example

P(A) Calculation

Percent Passed Test

Divisible by 3 Probability

Total Marbles

Probability of Combined Events

Defective Computers

Updated Probability after Selection

Union of Sets (AUB)

Intersection of Sets (AÇB)

Probability of an Event

Inclusive Events

Getting Even Numbers

Tossing a Coin (Probabilities)