Permutations and Combinations

Permutations and Combinations

by Steven Giesting

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​Example 1

​In how many ways can 15 runners finish first, second, and third?

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​Method 1: Fundamental Counting Principle

​15 x 14 x 13 = 2730

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​Method 2: Use the permutation formula

​₁₅P₃= 15!/(15-3)! = 2730

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​Example 2

​In a track invitational, the top 3 runners in each heat advance to the finals. If there are 8 runners in a heat, in how many ways can the runners advance?

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​Use the combination formula

​₈C₃ = 8!/(3!(8-3)!) = 8!/(3!*5!) = 56

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Multiple Choice

A salad bar offers eight choices of toppings for a salad.  In how many ways can you choose 4 toppings?  Is this a permutation or combination?

• permutation

• combination

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