Question: A baton is painted with three cylindrical bands of color (not necessarily distinct), with each band of the same length. (a) How many distinct paintings

A baton is painted with three cylindrical bands of color (not necessarily distinct), with each band of the same length.
(a) How many distinct paintings can be made if there are three colors of paint available? How many for four colors?
(b) Answer part (a) for batons with four cylindrical bands.
(c) Answer part (a) for batons with n cylindrical bands.
(d) Answer parts (a) and (b) if adjacent cylindrical bands are to have different colors.

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