Question

Suppose a designer has a palette of 14 colors to work with, and wants to design a flag with 4 vertical stripes, all of different colors.
How many possible flags can be created?

Answer 1

Answer:

182

The number of permutations of 14 things taken 2 at a time is ...

 14P2 = 14·13 = 182

The first color can be any of the 14 on the palette. The second color must be different, so can be any of the remaining 13.

___

We assume that a "yellow/red" flag is different from a "red/yellow" flag. That is, order matters.