Chapter 13.9, Problem 6PPS

To determine

To calculate: No. of ways can the runners finish in first, second and third place.

Answer to Problem 6PPS

There are $210$ ways that the runners can finish in the first, second and third place.

Explanation of Solution

Given information:

No of runners $7$ .

Calculation:

As given there are $7$ no. of runners.

So for finding out the ultimate objective that is no of ways runners finish,

A permutation is an arrangement or listing in which the order is important whereas selecting the first, second and third place order is important.

Thus, here permutation is used.

As there are $7$ runners, so there are $7$ choices for the first place.

  $6$ choices for the second place and $5$ choices for third place.

Thus, number of ways that the runners finish first, second and third place is as follows:

  $\begin{array}{l}P\left(7,3\right)=7\times 6\times 5\\ =210\end{array}$

Thus, there are $210$ ways that the runners can finish in the first, second and third place.