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Permutation of Alike Objects

There are two ways of permuting similar or like objects:

Case 1: Taken all at a time

Case 2: Taken some at a time

Suppose we have n distinct objects out of which n1 are of one type, n2 of second type and so on... nr are of r type, then the number of permutations is given by 

n!/ (n1)!(n2)! ….. (nr)!

This can be explained by the following diagram:

Number of permutation of n things

Then the number of permutations taken all at a time are given by n!/p!q!r!

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