In how many ways can a committee of 7 members be selected from 6 men and 5 women consisting of 4 men and 3 women?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 150
The order of the members does not matter in a committee, so each choice is a combination; the men and the women are chosen separately and the two counts are multiplied, since any group of men can go with any group of women.
4 men out of 6: \(\displaystyle ^6C_4={}^6C_2=\frac{6\times5}{2\times1}=15\)
3 women out of 5: \(\displaystyle ^5C_3={}^5C_2=\frac{5\times4}{2\times1}=10\)
Number of committees \(=15\times10=\) 150