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?

Question

Mathematics

Aylin Zavala

1 July, 00:35

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?

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Answers (1)

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Lina · 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.