Question

The number of ways in which a committee consisting of 3 men and 2 women, can be chose from 7 men and 5 women, is
(a) 45
(b) 350
(c) 4200
(d) 230

Answer 1

The selection of 5 members, consisting of 3 men and 2 women from 7 men and 5 women, can be made by selecting 3 men from 7 men and 2 women from 5 available
∴ This can be done in ⁷C₃ × ⁵C₂
$$\begin{gathered} =\frac{7!}{4!3!}\times \frac{5!}{3!2!} \\ =\frac{7\times 6\times 5\times 4!}{4!\times 3!}r\frac{5\times 4\times 3!}{3!\times 2!} \\ =\frac{7\times 6\times 5}{3\times 4}\times \frac{5\times 4}{2} \\ =35\times 10 \\ =350 \end{gathered}$$
Hence, the correct answer is option B.