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 $\frac{n!}{k!(n-k)!}$ ways.

$(^6 _3)=\frac{6!}{3!(6-3)!}=\frac{6!}{3! \times 3!}=\frac{3! \times 4 \times 5 \times 6}{3! \times 6}=4 \times 5=20$

There are 20 different 3-member groups.