In how many ways 3 flags of colors black, purple & yellow can be arranged at the corners of an equilateral triangle?
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There is only a very finite amount of possibilities... Try to find out the distinct cases:
This appears to me as a problem of circular permutation.
Fix one flag of any color (say black) at a particular corner of the specified equilateral triangle, then the other two flags (purple and yellow) can be arranged in $2!$ ways at the other two corners. Hence, the answer should be $4$.