Chapter 11.6, Problem 50E

To determine

To calculate: the ways to finish the race in first, second and third place by the eight horses.

Answer to Problem 50E

the ways to finish the race in first, second and third place by the eight horses is $336$ .

Explanation of Solution

Given :

Total number of horses = $8$

Formula used:

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

Calculation : tofind the number of ways we have to choose three horses among the eight horses,

So:

  $\begin{array}{l}P{}_3=\frac{8!}{\left(8-3\right)!}\text{ [substitute n by 8 and r by 3]}\\ P{}_3=\frac{8!}{5!}\text{ [subtract]}\\ P{}_3=336\text{ [expand factorial, divide out common factors and multiply]}\end{array}$

Hence,the ways to finish the race in first, second and third place by the eight horses is $336$ .