Hello, Vulcan!

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 bothHeandSheareon the committee.

HeandSheare 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 bothHeandSheserving.

Therefore, there are: . committees

. . in which bothHeandSheare not included.