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  • Numbers of ways in which the corners of an $n$-sided polygon can be colored with $2$ colors? (It is permissible to use a single color on all $n$ corners.)
  • Numbers of ways in which the corners of an $n$-sided polygon can be colored with $m$ colors? (It is permissible to use a single color on all $n$ corners.)

Note that Vertices are unlabelled.

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