The number of ways a committee consisting of 3 men and 1 woman can be formed from 5 men and 3 women, is _____
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30
The men and the woman are chosen separately, and by the fundamental principle of counting the two numbers of choices are multiplied. The order of choosing does not matter, so each choice is a combination, \({}^{n}C_{r}\).
3 men out of 5: \(\displaystyle {}^{5}C_{3}=\frac{5\times4\times3}{3\times2\times1}=10\)
1 woman out of 3: \({}^{3}C_{1}=3\)
Number of committees \(=10\times3=30\)