Chapter 13, Problem 35SGR

To determine

Calculate number of possible ways of making 3 numbers on a lock having 40 numbers..

Answer to Problem 35SGR

There are 9880 possible ways of making 3 numbers on a lock having 40 numbers.

Explanation of Solution

Given:

Total number on lock, n = 40

Numbers selected for combination, r = 3

Calculations:

Here, we have to calculate number of possible ways of making 3 numbers on a lock having 40 numbers.

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

  $\begin{array}{l}{}^n{C}_r=\frac{n!}{r!}\\ {}^{40}{C}_3=\frac{40\times 39\times 38}{1\times 2\times 3}\\ {}^{40}{C}_3=20\times 13\times 38\\ {}^{40}{C}_3=9880\end{array}$

There are 9880 possible ways of making 3 numbers on lock having 40 numbers.

Conclusion:

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