# Ten people are entered in a race. If there are no ties, in how many ways can the first three places come out?

P_(10,3)=(10!)/(7!)=10xx9xx8=720 ways

#### Explanation:

This is a permutation problem, in that we care about the order of finishers. The general formula is:

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

We have

P_(10,3)=(10!)/(7!)=10xx9xx8=720 ways