Question

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

Answer 1

`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