Chapter 12, Problem 4STP

To determine

To find: the ways of choosing the CDs.

Answer to Problem 4STP

The total number of ways are $6840$ of choosing the CDs.

Explanation of Solution

Given information:

Choose $20$ CDs from $3$ CDs.

Formula used:

  $\text{C}\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

Calculation: to find the different ways, first substituten by $20$ and r by $3$ in the formula, then expand the factorial and

  $\begin{array}{l}\text{C}\left(n,r\right)=\frac{n!}{\left(n-r\right)!}\\ \text{C}\left(20,3\right)=\frac{20!}{\left(20-3\right)!}\text{ [substitute]}\\ \text{C}\left(20,3\right)=\frac{20!}{17!}\text{ [subtract]}\\ \text{C}\left(20,3\right)=\frac{20·19·18·17!}{17!}\text{ [expand factorial]}\\ \text{C}\left(20,3\right)=20·19·18\text{ [simplify]}\\ \text{C}\left(20,3\right)=6840\text{ [multiply]}\end{array}$

Thus, the number of ways is $6840$ .