Question

There are 6 boys and 10 girls in a group. Find the number of ways a committee of 7 that can be formed where the president must be a boy and the vice-
president must be a girl.

Answer 1

The committee consists of 7 members - president, vice-president and 5 ordinary members.

The president must be a boy, so we can choose him in 6 ways. The vice-president must be a girl, so we can select her in 10 ways. Rest of the committee can be formed from 5 boys and 9 girls. So the number of way we can choose 5 members is $C(14,5)= 2002.$

The total number of way we can form the committee is $6\times 10 \times 2002 =120\,120$.