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