Out of 6 men and 4 women, a committee of 5 members is to be formed so that it has 2 women and 3 men. In how many different ways can it be done:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 120
The order in which members are picked does not matter in a committee, so each choice is a combination, \({}^{n}C_{r}\). The men and the women are chosen independently, so the two numbers of ways are multiplied.
3 men out of 6: \(\displaystyle {}^{6}C_{3}=\frac{6\times5\times4}{3\times2\times1}=20\)
2 women out of 4: \(\displaystyle {}^{4}C_{2}=\frac{4\times3}{2\times1}=6\)
Number of committees \(=20\times6=120\)