Counting Homework

Question

There are ten female board members and twenty male board members.

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

1. ways

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

1. ways

Determine the probability of selecting a committee of ten board members where exactly two of the members were female. Write your answer as a decimal, rounded to the nearest thousandth.

1. Answer: 

Answer 1

1.

( 30! ) / ( 20 ! ) / ( 10! ) = 30,045,015

This is a combination, so use the formula;

N! / R! / ( N- R )!

where N is the total number of choices to be taken in groups of R at a time. N ≥ R

2.

First use the above formula on a group of 2 women:

10! / 2! / 8! = 10 * 9 / 2 = 45

Then multiply it by a group of 8 men;

45 * 20! / 8! / 12! = 45 * 125,970 = 5,668,650

3.

Divide the answer to (2) above by the answer to (1) above:

5,668,650 / 30,045,015 ≈ 0.1886718978

which is 0.189 to the nearest thousandth.