Chapter 10.5, Problem 71E

To determine

To calculate:

Number of different sets of music types you choose for purchase.

Answer to Problem 71E

Number of different sets of music types you choose for purchase is $30$ .

Explanation of Solution

Given information:

  

Calculation:

The number of possible outcomes as the number of combinations of $5$ contemporary music CD taken $2$ at a time, $C{}_2$ because the order is not important.

Similarly, the classical CD can be chosen in $C{}_1$ ways.

Need to apply combination,

The expression for combination for $n$ objects $r$ at a time is given by,

  $C{}_r=\frac{n!}{\left(n-r\right)!.r!}$

The required numbers of combinations are as below,

  $\begin{array}{l}C{}_2.C{}_1=\frac{5!}{\left(5-2\right)!.2!}.\frac{3!}{\left(3-1\right)!.1!}\\ C{}_2.C{}_1=\frac{5!}{3!.2!}.\frac{3!}{2!.1!}\\ C{}_2.C{}_1=\frac{\mathrm{5.4.3}!}{3!\mathrm{.2.1}}.\frac{3.2!}{2!.1}\\ C{}_2.C{}_1=10.3\\ C{}_2.C{}_1=30\end{array}$

Thus, answer is $30$ .