Question

The student council at your school consists of 22 members. In how many ways can you select a committee of five members if
a) the president and the secretary must be included?
b) the vice-president must be excluded?

Answer 1

There are 22 members. A commitee of 5 members is needed.

a) the president and the secretary included. 20 members remain and the committee will need 3 members to be selected.

C(n, r) =$\frac {n!} {(n-r)! r!}$

C(20,3)= $\frac {20!}{(20-3)!3!}$

=1140 ways

b) vice president must be excluded

Eligible members will be 21 and 5 members need to be selected to form a commitee

C(n, r) = $\frac {n!} {(n-r)! r!}$

C(21,5)=$\frac {21!}{(21-5)!5!}$

=20349 ways