# Coach Ringdahl has 10 players on his varsity basketball team. How many different starting line-ups (5 players) can he choose?

252

#### Explanation:

This is a combinations question - we don't care about the order in which we select the 5 players in the starting line-up, only that they are chosen.

So we have:

C_(10,5)=(10!)/((5!)(10-5)!)=(10!)/((5!)(5!)

And now let's evaluate this:

(10!)/((5!)(5!))=(color(red)(cancel(10))xxcolor(green)(cancel9)^3xxcolor(blue)cancel(8)^2xx7xx6xxcancel5!)/((cancel5!)(color(red)(cancel5)xxcolor(blue)(cancel4)xxcolor(green)(cancel3)xxcolor(red)(cancel2)xx1))=3xx2xx7xx6=252