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
Geoff K.
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 #""_8C_3#, which is #(8!)/(3! xx 5!)=56#.

Of the 7 women available, we must choose 2. The number of possible groups is #""_7C_2#, which is #(7!)/(2! xx 5!)=21#.

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#

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