Answer
735 ways
Work Step by Step
Committee members are chosen with no importance of order of choice, so we deal with combinations.
We have a sequence of selections in which we choose
1. ... 4 men out of a group of 7 ... in ${}_{7}C_{4}$ ways
2. ... 5 women out of a group of 7 ... in ${}_{7}C_{5}$ ways
By the Fundamental Counting Principle,
Total ways= ${}_{7}C_{4}\cdot {}_{7}C_{5}$
${}_{7}C_{4}=\displaystyle \frac{7!}{(7-4)!4!}=\frac{7\times 6\times 5}{1\times 2\times 3}=35$
${}_{7}C_{5}=\displaystyle \frac{7!}{(7-5)!5!}=\frac{7\times 6}{1\times 2}=21$
Total = 35$\times$21 = 735 ways
