Question

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

Answer 1

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.