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)=
`(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)=
`(3!)/(2!(1)!)= (3*2*1)/(2*1)=3`

5. C(8, 6)=
`(8!)/(2!6!)= (8*7*6!)/(2*6!)= (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.