Suppose a designer has a palette of 14 colors to work with, and wants to design a flag with 2 vertical stripes, all of different colors.

How many possible flags can be created?

182

Step-by-step explanation:

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.

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