Chapter 10.5, Problem 39E

To determine

Tocalculate:

Total orders that bicyclists finish the race.

Answer to Problem 39E

Total $132600$ orders that bicyclists finish the race.

Explanation of Solution

Given information:

Total athlete’s: $52$

Formula used:

Expression for permutation

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

Where,

  $n=$ objects

  $r=$ time

Calculation:

There are total $52$ athlete’s competing for the race and it is required to know in how many ways bicyclists come first, second or third. So, the order is important.

So, now apply the permutation. The expression of permutation is as follows:

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

Therefore, the number of permutations is as follows:

  $\begin{array}{l}{}_{52}{P}_3=\frac{52!}{\left(52-3\right)!}\\ =\frac{52!}{49!}\\ =\frac{52\cdot 51\cdot 50\cdot 49!}{49!}\\ =132600\end{array}$

Thus, the value of ${}_{52}{P}_3$ is $132600$ .

Hence, there are $132600$ orders that bicyclists finish the race.