Question

a small acting club has 6 members. 3 of the members are to be chosen for a trip to see a Broadway play. how many different 3-member groups are possible

Answer 1

A group of k elements can be chosen from a group of n elements in
`(n!)/(k!(n-k)!)` ways.


`(^6 _3)=(6!)/(3!(6-3)!)=(6!)/(3! * 3!)=(3! * 4 * 5 * 6)/(3! * 6)=4 * 5=20`

There are 20 different 3-member groups.