Chapter 0, Problem 17PR

To determine

To find: Whether the permutation or combination can be used in the provided situation. Also, solve the provided situation.

Answer to Problem 17PR

Combination could be used here.

Explanation of Solution

Given:

It is required to select 3 flavours out of the 15 flavours of the juice.

Concept used:

Combination is used when the order of the selection does not matter.

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

Calculation:

Here, order is not a matter of fact. Thus, the combination could be used here.

The required number of ways could be calculated as:

  $\begin{array}{c}C{}_3=\frac{15!}{12!\left(15-12\right)!}\\ =\frac{15\times 14\times 13\times \bcancel{12!}}{\bcancel{12!}\left(3\right)!}\\ =455\end{array}$

Thus, the number of ways is 455.