Permutation of identical elements

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The discussion focuses on calculating permutations of identical elements using binomial coefficients. Specifically, when dealing with n objects where n1, n2, ..., nk are identical, the formula involves using binomial coefficients to determine the arrangements. For instance, the example provided illustrates that there are (5 choose 3) or (5 choose 2) permutations for the sequence (1,1,1,2,2). This method effectively simplifies the calculation by ignoring the last factor, which is always 1.

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If we have n object and n1,n2,..nk are identical element. And we take r at a time i.e r < n. Is there a general formulae for the permutation of the above. Or how it is solved? Thanks.
 
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Use the binomial coefficients to find the ways to arrange the identical element - one factor per set of identical elements. The last factor is 1 and can be ignored.

As an example, there are (5 choose 3)=(5 choose 2) different permutations of (1,1,1,2,2).
 

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