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)=[tex] \frac{n!}{r!(n-r)!} [/tex]
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)=[tex]\frac{3!}{2!(1)!}= \frac{3*2*1}{2*1}=3 [/tex]
5. C(8, 6)=[tex]\frac{8!}{2!6!}= \frac{8*7*6!}{2*6!}= \frac{8*7}{2}= 4*7=28[/tex]
So there are C(8,6)=28 ways of chosing 6 out of 8 people to form the subcommittees.
