Question

There are 8 members on a board of directors. if they must form a subcommittee of 6 members, how many different subcommittees are possible?720 28 20,160 262,144

Answer 1

1. Given a group of n people. There are C(n, r) ways of forming groups of r out of n.

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

3. For example, given {Andy, John, Julia}. We want to pick 2 people to give a gift: we can pick {(Andy, John), (Andy, Julia), (John, Julia)}, so there are 3 ways. So we can list and count.

4. Or we could do this with the formula C(3, 2)=$\frac{3!}{2!(1)!}= \frac{3*2*1}{2*1}=3$

5. C(8, 6)=$\frac{8!}{2!6!}= \frac{8*7*6!}{2*6!}= \frac{8*7}{2}= 4*7=28$

So there are C(8,6)=28 ways of chosing 6 out of 8 people to form the subcommittees. <span />