Chapter 13, Problem 34SGR

To determine

Calculate number of possible ways a five runners can complete first, second or third position.

Answer to Problem 34SGR

There are 60 possible ways a five runners can complete first, second or third position.

Explanation of Solution

Given:

Total number of runners, n = 5

Numbers of positions required to complete by runners, r = 3(first, second or third place that is 3)

Calculations:

Here, we have to calculate number of possible ways a five runners can complete first, second or third position.

It is an example of permutations, as there are n different choices for selecting r.

  $\begin{array}{l}{}^n{C}_r=n\times (n-1)\times (n-2)\\ {}^5{C}_3=5\times 4\times 3\\ {}^5{C}_3=60\end{array}$

There are 60 ways, a five runners can occupy first, second or third place.

Conclusion:

Therefore, we are able to calculate possible methods to select r numbers from given n numbers.