Question

Joe has 13 different cars. He wants to reward some of his employeesby giving away some of the cars from his collection. If he gives a car tohis Regional Manager, Division Supervisor, and Local Supervisor at anupcoming corporate event, how many ways can this be done?

Answer 1

$\begin{gathered} \text{ In this case we use the combination of C(n,k) where n is the number of cars, and k the } \\ \text{size of the group} \\ C(n,k)=\frac{n!}{k!(n-k)!} \\ \text{ So we must compute} \\ C(13,3)=\frac{13!}{3!(13-3)!} \\ C(13,3)=\frac{13!}{3!(10!)} \\ C(13,3)=\frac{13\cdot12\cdot11}{3\cdot2} \\ C(13,3)=286 \end{gathered}$

He can give the cars 286 ways