Question

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

Answer 1

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`