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We have $n$ types of objects, and the number of objects of type $i$ is $a_i$, $1\leq i\leq n$.

What is the number of permutation of the $\sum_{i=1}^n a_i$ objects, if no two objects of the same type are next to each other?

A simple example: If we have the objects $\{a,a,a,b,b,c,c\}$, then we allow $abcabac$ but not $aaabbcc$.

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    Interesting quite non-standard question. It may be difficult.2012-03-14
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    This reminds me of concepts from Lara K. Pudwell's PhD thesis.2012-05-29
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    Do you distinguish between objects of the same type? In other words, is there *one* possible arrangement $aba$ or are there two because the two objects of type $a$ are nevertheless distinct and swapping them leads to another permutation?2013-03-22
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    @MvG, as Joel Adler was last seen a month ago and I am the bounty holder, I think the language suggests that each object of type $a$ should be indistinguishable.2013-03-23
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    Also, is there a method that uses the Principle of Inclusion and Exclusion? I understand that it may be tedious in the general case, but in this specific case I feel it would be more illuminating.2013-03-24

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