There are 9 female board members and 21 male board members. How many ways are there to make a committee of 17 board members? How many ways are there to make a committee of 17 board members if exactly 6 must be female?

There are 119,759,850 ways to make a committee of 17 board members.

There are 29,628,144 ways to make a committee of 17 board members if exactly 6 must be female

Step-by-step explanation:

The order that the people are chosen for the committee is not important. So we use the combinations formula to solve this question.

Combinations formula:

is the number of different combinations of x objects from a

set of n elements, given by the following formula.

How many ways are there to make a committee of 17 board members?

17 from a set of 30. So

There are 119,759,850 ways to make a committee of 17 board members.

How many ways are there to make a committee of 17 board members if exactly 6 must be female?

6 female(from a set of 9) and 11 male(from a set of 21). So

There are 29,628,144 ways to make a committee of 17 board members if exactly 6 must be female

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step-by-step explanation:

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