Podcast
Questions and Answers
The formula for permutations is nPr = ______ / (______ - ______)!, where n is the total number of items and r is the number of items being chosen. Permutations are used when the order of the selection ______ matter.
The formula for permutations is nPr = ______ / (______ - ______)!, where n is the total number of items and r is the number of items being chosen. Permutations are used when the order of the selection ______ matter.
A bag contains 3 red and 7 blue balls. What is the probability of drawing a red ball and then a blue ball without replacement?
A bag contains 3 red and 7 blue balls. What is the probability of drawing a red ball and then a blue ball without replacement?
If two dice are rolled, the probability of getting a sum greater than 9 is ______.
If two dice are rolled, the probability of getting a sum greater than 9 is ______.
1/6
The probability of drawing two face cards in a row from a deck without replacement is the same as drawing one face card and then another face card with replacement.
The probability of drawing two face cards in a row from a deck without replacement is the same as drawing one face card and then another face card with replacement.
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A box has 5 defective and 15 non-defective items. What is the probability of randomly picking two non-defective items in a row without replacement?
A box has 5 defective and 15 non-defective items. What is the probability of randomly picking two non-defective items in a row without replacement?
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Match the following probability scenarios with their corresponding formulas:
Match the following probability scenarios with their corresponding formulas:
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How many ways can the letters in 'SUCCESS' be arranged?
How many ways can the letters in 'SUCCESS' be arranged?
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A box contains 3 identical red and 4 identical green balls. How many ways can they be arranged? ______
A box contains 3 identical red and 4 identical green balls. How many ways can they be arranged? ______
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The number of ways to arrange 7 identical books and 3 different books on a shelf is the same as the number of ways to arrange 10 different books on a shelf.
The number of ways to arrange 7 identical books and 3 different books on a shelf is the same as the number of ways to arrange 10 different books on a shelf.
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How many different ways can 5 people be seated in a row?
How many different ways can 5 people be seated in a row?
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The probability of drawing an ace from a standard deck of 52 cards is 1/13.
The probability of drawing an ace from a standard deck of 52 cards is 1/13.
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What is the probability of rolling a 5 on a fair 6-sided die?
What is the probability of rolling a 5 on a fair 6-sided die?
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If two dice are rolled, the probability that the sum is 7 is __________.
If two dice are rolled, the probability that the sum is 7 is __________.
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Match the situation with the correct number of arrangements or combinations:
Match the situation with the correct number of arrangements or combinations:
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How many ways can a 4-digit code be formed if digits can repeat?
How many ways can a 4-digit code be formed if digits can repeat?
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The probability of flipping at least one heads in two flips of a fair coin is 0.75.
The probability of flipping at least one heads in two flips of a fair coin is 0.75.
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In how many ways can the top 3 finishers be arranged in a race with 8 runners?
In how many ways can the top 3 finishers be arranged in a race with 8 runners?
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Flashcards
Probability of King or Heart
Probability of King or Heart
Probability of drawing a King or a Heart from a deck of cards.
Rolling Die Probability
Rolling Die Probability
Probability of rolling a 6 followed by an even number on dice.
Drawing Face Cards
Drawing Face Cards
Probability of drawing two face cards in a row without replacement.
Drawing Red and Blue Balls
Drawing Red and Blue Balls
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Sum of Dice Greater than 9
Sum of Dice Greater than 9
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Selecting Girls from Class
Selecting Girls from Class
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Arranging Letters in 'SUCCESS'
Arranging Letters in 'SUCCESS'
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Identical Balls Arrangement
Identical Balls Arrangement
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Permutations Formula
Permutations Formula
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Combinations Formula
Combinations Formula
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Probability of Rolling 5
Probability of Rolling 5
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Probability of Flipping Heads
Probability of Flipping Heads
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Probability of Event Not Happening
Probability of Event Not Happening
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Arrangements of MATH
Arrangements of MATH
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Choosing 4 from 12
Choosing 4 from 12
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Chair and Vice Chair Selection
Chair and Vice Chair Selection
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Study Notes
Permutations and Combinations Formulas
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Permutations: Arrange n distinct objects in r positions. Formula: P(n, r) = n! / (n-r)! Use when order matters.
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Combinations: Choose r objects from a set of n distinct objects. Formula: C(n, r) = n! / (r! * (n-r)!) Use when order does not matter.
Basic Probability Concepts
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Probability of an event: A numerical measure of the likelihood of an event occurring. Value ranges from 0 (impossible) to 1 (certain).
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Complement of an event: The probability of an event not occurring is 1 minus the probability of it occurring.
Simple Examples
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Arranging 6 books: 6! = 720 ways
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Choosing 4 members from 12: C(12, 4) = 495 ways
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Rolling a 5 on a fair die: 1/6
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Flipping heads: 1/2
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Probability of an event not occurring (0.25 probability): 1 - 0.25 = 0.75
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Drawing an ace: 4/52 = 1/13
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Arranging letters in "MATH": 4! = 24 ways
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Probability of a certain event: 1
Situational Permutations and Combinations
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Committee of 3 from 10: C(10, 3) = 120 ways
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3-digit code from 0-9 (no repeats): P(10, 3) = 720 possible codes
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Top 3 finishers in 8-runner race: P(8, 3) = 336 ways
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5 people seated in a row, 2 together: (4!) * 2! = 48 ways
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President and Vice-President from 6 candidates: P(6, 2) = 30 ways
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4-digit code with repeats allowed: 10 * 10 * 10 * 10 = 10,000 ways
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5 students arranged in a line: 5! = 120 ways
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2-person leadership team from 7: C(7, 2) = 21 ways
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Answering 8 multiple-choice questions (4 choices each): 4^8 = 65,536 ways
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Choosing 3 students from 20: C(20, 3) = 1140 ways
Probability with Dice, Coins, and Cards
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Sum of 7 when rolling two dice: 6/36 = 1/6
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Possible sequences of heads and tails in 4 flips: 2^4 = 16
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Probability of rolling a prime number (2, 3, 5): 3/6= 1/2
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Probability of drawing a red marble: 4 / (4+5+6) = 4/15
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Probability of drawing all 5 hearts: (13/52) * (12/51) * (11/50) * (10/49) * (9/48) = very low
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Probability of at least one heads in two flips: 1 - (1/4) = 3/4
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Probability of at least one 3 when rolling two dice: 1- (5/6 * 5/6) =11/36
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Probability of drawing a king or a heart: (4/52) + (13/52) - (1/52) = 16/52
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Probability of 6 followed by even number: (1/6) * (3/6) = 1/12
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Probability of drawing two face cards: (12/52) * (11/51)
Compound Probability and Dependent Events
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Probability of red ball then blue ball (without replacement): (3/10) * (7/9) = 21/90
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Probability of two spades: (13/52) * (12/51)
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Probability of sum greater than 9 with two dice: (4/36)
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Probability of two non-defective items: (15/20) * (14/19)
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Probability of rolling a 2 or 5: (2/6) = 1/3
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Probability of three 6s in a row: (1/6)^3 = 1/216
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Probability of at least one tails (2 coin flips): 1 - (1/4) = 3/4
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Probability of all three students being boys (20 students total, 10 boys, 10 girls): ((10/20) * (9/19) * (8/18))
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Probability of doubles and heads (2 dice, 1 coin): (6/36) * (1/2) = 1/12
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Probability of two girls from a class of 100 students (60 boys, 40 girls): (40/100) * (39/99)
Distinguishable and Non-Distinguishable Arrangements
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Arrangements of "SUCCESS": 7! / 3! = 840
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Arrangements of "BALLOON": 7! / 2! 2! = 1260
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Arrangements of 5 red & 4 blue balls: (9! / 5! , 4!) = 126 ways
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Arrangements of "PEPPER": 6! / 3! = 120 ways
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3 red & 4 green balls:(7! / 3! , 4!) = 35 ways
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7 identical & 3 different books arrangement on a shelf: you can treat 7 identical books as one unique and total arrangements will be (10! / 7!)
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10 students lined up, 4 twins: treat 4 twins as one person. Total is (7! * 4!)
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"MISSISSIPPI" arrangements: 11! / 4! * 4! * 2! =34,650
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Flag with 3 red, 2 blue, & 2 green stripes: 7! / 3! 2! 2! = 210 ways
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8 books (3 identical math & 5 different): treat the identical 3 as 1 and use the formula (9! / 3!)
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Description
Explore the fundamental concepts of permutations and combinations through essential formulas and probability rules. This quiz will challenge your understanding of arranging objects and calculating probabilities with practical examples. Put your knowledge to the test!
