Question

A committee of 5 members in to be formed from 8 men and 6 women Find the number of ways of forming the commiltee if it has to contain 3 men and 2 women:

• A. 420
• B. 210
• C. 840
• D. 1220

Answer 1

Answer: (C)

840

Number of ways in which$3$ men can be chosen from $8$ men and $2$ women can be chosen from $6$ women is
${}^8{C}_3{\times }^6{C}_2=\frac{8!}{3!(8-3)!}\times \frac{6!}{2!(6-2)!}=\frac{8!}{3!\left(5\right)!}\times \frac{6!}{2!\left(4\right)!}=\frac{8\times 7\times 6\times 5!}{3\times 2\times 5!}\times \frac{6\times 5\times 4!}{2\times 1\times 4!}=56\times 15=840$
Here we applied the formula ${}^n{C}_r=\frac{n!}{r!(n-r)!}$