Question

The league championship 800 meter race has 6 runners.

In how many different ways they place first, second, and third?

Answer 1

Answer: 120

Explanation:

Given : The league championship 800 meter race has 6 runners.

The number of positions = 3

Since order matters here , so we use Permutation.

The permutation of n things taking r at a time is given by :-

`^nP_r=(n!)/((n-r)!)`

Then, the number of different ways they place first, second, and third :_

`^6P_3=(6!)/((6-3)!)=(6*5*4*3!)/(3!)=120`

Hence, they can place first, second, and third in 120 different ways .