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Main Idea and Vocabulary Example 1: Find a Permutation Example 2: Real-World Example: Find Probability Lesson Menu

Find the number of permutations of a set of objects and find probabilities. Main Idea/Vocabulary

Find a Permutation BOWLING A team of bowlers has five members who bowl one at a time. In how many orders can they bowl? Find the number of possible orders using the Fundamental Counting Principle. There are 5 choices for the 1st bowler, 4 choices for the 2nd bowler, 3 choices for the 3rd bowler, 2 choices for the 4th bowler, and 1 choice for the 5th bowler. 5 ● 4 ● 3 ● 2 ● 1 = 120 Answer: There are 120 orders in which the five members of the bowling team can bowl. Example 1

TRACK AND FIELD A relay team has four members who run one at a time TRACK AND FIELD A relay team has four members who run one at a time. In how many orders can they run? A. 1 order B. 4 orders C. 16 orders D. 24 orders Example 1

7 ● 6 ● 5 = 210 ← The number of permutations of 3 places Find Probability RAFFLE A school fair holds a raffle with 1st, 2nd, and 3rd prizes. Seven people enter the raffle, including Marcos, Lilly, and Heather. What is the probability that Marcos will win the 1st prize, Lilly will win the 2nd prize, and Heather will win the 3rd prize? 7 ● 6 ● 5 = 210 ← The number of permutations of 3 places There are 7 choices for first place. There are 6 choices for second place and 5 for third. Example 2

Find Probability There are 210 possible arrangements, or permutations, of the 2 places. Since there is only one way of arranging Marcos, Lilly, and Heather in 1st, 2nd, and 3rd place respectively, the probability of this event is Answer: Example 2

CLUBS The president and vice-president of the French Club will be randomly selected from a jar of 24 names. Find the probability that Sophie will be selected as president and Peter selected as vice-president. A. B. C. D. Example 2

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