In a group of ten girls and eight boys on the prom committee two of each must be chosen for the decoration committee. One of the decoration committee members will then be chosen as the leader of the committee. In how many ways can this committee be chosen?
+2668 The girls can be chosen in \({10 \choose 2}\) ways. The boys can be chosen in \(8 \choose 2\) ways. of the 4 members, there is 4 ways to choose a leader.
So... the answer is \({10 \choose 2} \times {8 \choose 2} \times 4 = 5040\) ways.
