Undergrad Permutation of identical elements

[rajeshmarndi]

If we have n object and n₁,n₂,..n_k 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.

 

[mfb]

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).