Chapter 12.6, Problem 2P

To determine

To calculate: The number of ways in which swimmers be assigned lanes for race.

Answer to Problem 2P

The number of ways are $40,320$ .

Explanation of Solution

Given information:

A swimming pool has 8 lanes.

Formula used:

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question,

There are 8 lanes.

This implies that first swimmer has 8 choices to lane , second swimmer has 7 choices , third swimmer has 6 choices and so on .

  $\begin{array}{l}=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\\ =40,320\end{array}$

Hence, the number of ways are $40,320$ .