SOLUTION: There are 13 female board members and 17 male board members. How many ways are there to make a committee of 18 board members? How many ways are there to make a committee of 1

Question 1195072: There are 13 female board members and 17 male board members.
How many ways are there to make a committee of 18 board members?
How many ways are there to make a committee of 18 board members if exactly 7 must be female?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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There are 13 female board members and 17 male board members.
(a) How many ways are there to make a committee of 18 board members?
(b) How many ways are there to make a committee of 18 board members if exactly 7 must be female?
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Part (a)

There are 13 + 17 = 30 board members, in all.


There are    different ways to select a committee of 18 board members.


Here    is the number of combinations of 30 persons taken 18 at a time.


The formula to calculate it is this


     =  =  =  = 86493225.    ANSWER

Part (b)

A committee of 18 board members, which includes 7 females, should include  18-7 = 11 males.


7 females from 13 females can be chosen in   = 1716 different ways.

11 males  from 17   males can be chosen in   = 12376 different ways.


Combining these different teams, consisting of 11 males and 7 females, 

we have 1716*12376 = 21237216 different ways to make such a committee which is required in part (b).

Solved.

----------------

This problem is on COMBINATIONS.

On Combinations, see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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