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

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=(13!)/(\mleft(13-5\mright)!) \\ =(13*12*11*10*9*8!)/(8!) \\ =13*12*11*10*9 \\ =154,440\text{ } \end{gathered}`

Hence the answer is 154,440 possible flags