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

Fill in the Blanks

Ten students are in a race. First, second, and third places will win medals. In how many ways can 10 runners finish first, second, and third (no ties allowed)?

​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

Fill in the Blanks

In the movie Hoosiers, how many lineups can coach Dale make from his roster?

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

Fill in the Blanks

In the show Ted Lasso, how many different starting lineups of 11 players can coach Lasso and Beard choose from if they have 23 players on the AFC Richmond roster?