Chapter 13, Problem 15RE

Choosing a Team In how many ways can a squad of 4 relay runners be chosen from a track team of 8 runners?

To determine

To find: In how many ways can a squad of 4 relay runners be chosen from a track team of 8 runners?

Answer to Problem 15RE

1680

Explanation of Solution

Given:

A squad of 4 relay runners to be chosen from a track team of 8 runners.

Formula used:

$P\left(n, r\right) = \frac{n!}{\left(n - r\right)!}$

Calculation:

we need to choose 4 relay runners from a track of 8 runners.

Here order is significant hence this is a case of permutation.

Number of ways 4 relay runners can be chosen from track of 8 runners is given by $P\left(8, 4\right)$.

$P\left(8, 4\right) = \frac{8!}{\left(8 - 4\right)!} = \frac{8!}{4!}$

$= 8*7*6*5*\frac{4!}{4!}$

$= 8*7*6*5$

$= 1680$

There are 1680 ways a squad of 4 relay runners can be chosen from track of 8 runners.