Answer
There are 1140 ways of selecting three CDs from a set of 20 CDs
Work Step by Step
We know that the order in which the three CD’s are selected does not make a difference since all would be taken for the vacation at the same time.
Since the order of the arrangement does not make a difference, we solve the problem with combinations..
The three CD’s are to be selected from a group of twenty CD’s. So, $ n=20,r=3$.
Hence,
$\begin{align}
& _{20}{{C}_{3}}=\frac{20!}{3!\left( 20-3 \right)!} \\
& =\frac{20!}{3!17!} \\
& =\frac{20\times 19\times 18\times 17!}{6\times 17!} \\
& =1140
\end{align}$
