Question

Suppose a designer has a palette of 13 colors to work with, and wants to design a flag with 5 vertical stripes, all of different colors.How many possible flags can be created?

Answer 1

SOLUTION

From this question, for this to be, it means the designer wants to arrange 13 colors of the palette by taking 5 vertical stripes at a time, all of different colours.

That is arranging 13, taking 5 at a time.

So, this is permutation or arrangement.

This is calculated as

$\begin{gathered} ^{13}P_5 \\ ^{13}P_5=\frac{13!}{\mleft(13-5\mright)!} \\ =\frac{13\times12\times11\times10\times9\times8!}{8!} \\ =13\times12\times11\times10\times9 \\ =154,440\text{ } \end{gathered}$

Hence the answer is 154,440 possible flags