Chapter 9.1, Problem 29E

Solution

To state: The number of different sets of discs that can be purchased by Juan if only three of the 48 compact discs available.

The resultant sets of compact discs are $17296$ .

Given information:

The number of sets of discs he purchased if only three of the 48 compact discs available.

Explanation:

Consider the given information.

He can purchase the sets of compact discs if only 3 of the 48 compact discs available.

By using combination counting formula the total number of ways that can combine n objects taken r at a time is given by:

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

Total number of compact discs: 48

Number of compact discs required: 3

  $\begin{array}{c}{C}_{{48}_3}=\frac{48!}{3!\left(48-3\right)!}\\ =\frac{48!}{3!45!}\\ =\frac{48\cdot 47\cdot 46\cdot 45!}{3!45!}\\ =\frac{48\cdot 47\cdot 46}{3\cdot 2\cdot 1}\\ =\frac{103776}{6}\\ =17,296\end{array}$

Now the total possible sets of compact discs are $C_{{48}_3}=17296$ .

Therefore, Juan can purchase $17,296$ sets of compact discs.