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Published byRalf Poole Modified over 9 years ago

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EXAMPLE 1 Counting Permutations Music You have five CDs. You can use the counting principle to count the number of permutations of 5 CDs. This is the number of different orders in which you can listen to the CDs. Choices for 1st CD Choices for 2nd CD Choices for 3rd CD Choices for 4th CD Choices for 5th CD 5 4 3 2 1 = 120 ANSWER You can listen to the CDs in 120 different orders.

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EXAMPLE 2 Counting Permutations Band Competition Twelve marching bands are entered in a competition. You can use the counting principle to count how many ways first, second, and third places can be awarded. Choices for 1st place Choices for 2nd place Choices for 3rd place 12 11 10 = 1320 Counting principle ANSWER There are 1320 ways to award the three places.

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GUIDED PRACTICE for Examples 1 and 2 1. Evaluate 3!. 3! = 3 2 1 = 6 2. Evaluate 6!. 6! = 6 5 4 3 2 1 = 720 3. Evaluate 1!. 1! = 1

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GUIDED PRACTICE for Examples 1 and 2 4. Chris wants to see four movies that were released in the past month. In how many different orders can Chris watch the movies? Choices for 1st place Choices for 2nd place Choices for 3rd place Choices for 4th place 4 3 2 1 = 24 Counting principle Chris can watch the movies in 24 different orders. ANSWER

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GUIDED PRACTICE for Examples 1 and 2 5. In how many ways can 7 runners finish in first, second, and third place? Choices for first Choices for second Choices for third 7 6 5 = 210 Counting principle ANSWER There are 210 ways to finish the first, second, and third place.

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