A committee of 5 members is to be formed by selecting out of 6 men and 4 women. In how many different ways the committee can be formed if it should have at least 2 women?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 186
The order of the members does not matter in a committee, so each choice is a combination. “At least 2 women” means the committee of 5 has 2, 3 or 4 women; the ways for each case are counted and added.
2 women and 3 men: \({}^{4}C_{2}\times{}^{6}C_{3}=6\times20=120\)
3 women and 2 men: \({}^{4}C_{3}\times{}^{6}C_{2}=4\times15=60\)
4 women and 1 man: \({}^{4}C_{4}\times{}^{6}C_{1}=1\times6=6\)
Total: \(120+60+6=\) 186