Chapter 13.10, Problem 38SR

To determine

The statement is permutation or combination then solve.

How many ways you can buy $2$ DVD’s from a display of $15$ ?

Answer to Problem 38SR

There are $105$ ways you can buy $2$ DVD’s from a display of $15$ .

Explanation of Solution

Calculation:

This is the combination situation because here the order is not prioritized as the person can choose $2$ DVD’s from the $15$ .

So the number of ways are as follows:

  $\begin{array}{l}C\left(15,2\right)=\frac{15!}{2!\times \left(15-2\right)!}\\ C\left(15,2\right)=\frac{15\times 14\times 13!}{2\times 1\times 13!}\\ C\left(15,2\right)=15\times 7\\ C\left(15,2\right)=105\end{array}$

So there are $105$ ways you can buy $2$ DVD’s from a display of $15$ .

Conclusion:

Hence, there are $105$ ways you can buy $2$ DVD’s from a display of $15$ .