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... n_r are of r type, then the number of permutations is given by 

n!/ (n₁)!(n₂)! ….. (n_r)!

This can be explained by the following diagram:

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