Chapter 8, Problem 73CR

To determine

To find: The different number of ways in which the bicyclists finish the race.

Answer to Problem 73CR

The different number of ways in which the bicyclists finish the race. is $479001600$ .

Explanation of Solution

Given information:

  $\text{The number of bicyclists entered the race}=12$ .

Formula used:

According to the mathematical principle of counting, the number of ways of filling $m$ slots out of $n$ elements is,

  $\text{Number}\text{of}\text{ways}=n\left(n-1\right)\left(n-2\right)\cdot \cdot \cdot \cdot \cdot \cdot \cdot .\left(n-m+1\right)$

Here, $m<n$ .

Calculation:

Calculate the number of possible ways as follows:

  $\begin{array}{c}\text{Number}\text{of}\text{ways}=12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\\ =479001600\end{array}$

Hence, the number of ways in which the bicyclists finish the race is $479001600$ .