# How many was can 10 people come in 1st, 2nd and 3rd place in a race once around the track?

Feb 7, 2016

Since order matters in this problem, we use the permutation formula.

#### Explanation:

Assuming P represents the number of outcomes, n the number of competitors and r the number of places to be awarded.

P = (n!)/((n - r)!

P = (10!)/((10 - 3)!)

P = (10!)/(7!)

Calculating using a calculator:

P = 720

There are 720 different outcomes possible in the race.