Question

There are nine men and ten women in a club; in how many ways can a committee of four be formed to include at least 1 man?

Answer 1

The number of combinations of the 19 people taken 4 at a time is:
19C4 = 3876.
The number of combinations with no men is:
10C4 = 210.
Therefore the number of ways of forming a committee of four including at least one man is:
3876 - 210 = 3666.
The answer is 3666 ways.