Chapter 13, Problem 36SGR

To determine

Calculate number of possible ways of selecting 8 prices from 20 choices.

Answer to Problem 36SGR

There are 125970 possible ways of selecting 8 prices from 20 choices.

Explanation of Solution

Given:

Total number of choices, n = 20

Number of prizes to be selected, r = 8

Calculations:

Here, we have to calculate number of possible ways of selecting 8 prices from 20 choices.

A combination is nothing but selecting r number of objects from different n number of objects. Hence, it is an example of combination.

  $\begin{array}{l}{}^n{C}_r=\frac{n!}{r!}\\ {}^{20}{C}_8=\frac{20\times 19\times 18\times 17\times 16\times 15\times 14\times 13}{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8}\\ {}^{20}{C}_8=5\times 19\times 3\times 17\times 2\times 13\\ {}^{20}{C}_8=125970\end{array}$

There are 125970 possible ways of selecting 8 prices from 20 choices.

Conclusion:

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