# How many ways can a committee of 3 men and 2 women be chosen from a pool of 8 men and 7 women?

##### 1 Answer

Apr 11, 2017

There are 1,176 different possible committees.

#### Explanation:

Let's break this down into the two sub-groups: one with men, and one with women.

Of the 8 men available, we must choose 3. The number of possible groups is

Of the 7 women available, we must choose 2. The number of possible groups is

Finally, each of the 56 possible sub-groups of only men could be paired with each of the 21 possible sub-groups of only women. That means the final number of possible committees is the *product* of these two values.

Our final answer is

#" "_8C_3 xx ""_7C_2#

# = 56 xx 21#

#=1176#