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Circular permutation of $k$ types of items on $n$ places with no two adjacent items of the same type. [duplicate]

Possible Duplicate: In how many ways we can put $r$ distinct objects into $n$ baskets? I have been trying to work out a problem but cannot get any closed formula or recurrence. You are ...
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Number of permutations with a certain number of fixpoints

Given a set of $n$ mutually distinct elements, how many permutations are there such that exactly $k$ of the permuted elements stay at the same place? Example Let's take the set $\{A,B,C,D\}$. The ...