From a group of 8 women and 6 men,
a committee consisting of 3 men and 3 women is to be formed.
How many different committees are possible
if 1 man and 1 woman refuse to serve together?
With no restrictions, there are: . possible committees.
We will count the cases in which both He and She are on the committee.
He and She are already on the committee.
We choose 2 more women from the remaining 7 women: ways.
We choose 2 more men from the remaining 5 men: ways.
Hence, there are: . committees with both He and She serving.
Therefore, there are: . committees
. . in which both He and She are not included.