15.3 Permutations and Combinations. Warm-up Suppose a club with 5 members wishes to choose a president, vice president and treasurer. In how many ways.

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Presentation transcript:

15.3 Permutations and Combinations

Warm-up Suppose a club with 5 members wishes to choose a president, vice president and treasurer. In how many ways can this be done?

Answer

Now suppose a club with 5 members wishes to choose a leadership council of 3 members. How many ways can this be done?

Answer

In the first situation, where order matters, each selection is called a permutation of 3 people from a set of 5. In the second situation, where order is not important, each selection is called a combination of 3 people from a set of 5.

Permutation Order matters = n(n-1)…(n - r + 1)

Combination Order does not matter n C k =

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1. Selecting three toppings for ice cream

2. Selecting the starting players for a basketball game.

3. Selecting three students to call on for answers.

4. Ranking your two favorite musical groups.

5. Selecting four toppings for a hot dog.

6. Selecting four ingredients for a soup.

7. Selecting three officers for a club.

8. Selecting three operations to be used to solve.

9. Selecting three students to speak at graduation.