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#