How many ways can you rearrange the letters in BANANA so that no letter winds up in the same spot?
Clarification: The A's and N's are indistinguishable, so in the new arrangement, AAANBN would be no good since the second letter is still an A.
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The resulting string of letters can't have an A in the 2nd, 4th, or 6th spot, so an A must be in the 1st, 3rd and 5th spot, leaving only 3 possible combinations, ABANAN, ANABAN, and ANANAB.