How many ways can you rearrange the letters in BANANA so that no letter winds up in the same spot?
There are 3×2×1 = 6 ways to rearrange the A's and 2×1 = 2 ways to rearrange the N's.
So, there are: 720/(6×2) = 720/12 = 60 ways to rearrange all the letters in BANANA.
As the 'A's cannot be at the same position it was before, the resulting arrangement must be AXAXAX, where X is one of the remaining letters.
We can only change the arrangement by considering permutations of "BNN", as the A's are already fixed.
As same letters are indistinguishable, the order does not matter. That means the only possible ways to rearrange the letters are "ABANAN", "ANABAN", and "ANANAB". There are only 3 ways in total.