Question

How many different nine player batting orders can be chosen from a baseball team of 16?

Answer 1

This problem is basically $_{16}P_9$

$_nP_r = \frac{n!}{(n - r)!}$

If I plug in n = 16 and r = 9

$\frac{16!}{(16-9)!} = \frac{16!}{7!} = 4151347200$

So there are 4151347200 different nine player batting orders that can be chosen from a baseball team of 16 :)