Chapter 13, Problem 16PT

To determine

Calculate number of possible ways to select 3 from 12 different names of an envelope

Answer to Problem 16PT

There are 220 possible ways to select 3 from 12 different names of an envelope.

Explanation of Solution

Given:

Envelope consist 12 different names, n = 12

Number of names required to selected, r = 3

Calculations:

Here, we have to calculate number of possible ways to select 3 from 12 different names of envelope.

A combination is nothing but selecting r number of objects from different n number of objects.

  $\begin{array}{l}{}^n{C}_r=\frac{n!}{r!}\\ {}^{12}{C}_3=\frac{12\times 11\times 10}{1\times 2\times 3}\\ {}^{12}{C}_3=2\times 11\times 10\\ {}^{12}{C}_3=220\end{array}$

There are 220 possible ways to select 3 manes from 12 different names of envelope.

Conclusion:

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