Question

How many ways can a baseball manager make a 9-player batting order from a group of 16 players?

Answer 1

4,151,347,200

Explanation:

This is a permutation question because we care about the order of the players in the batting order. The general formula for a permutation is:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

We have `n=16, k=9`

`P_(16,9)=(16!)/(7!)=16xx15xx14xx13xx12xx11xx10xx9xx8=4,151,347,200`