We shall now determine the number of permutations of a set of *n* objects when
certain of the objects are indistinguishable from each other. To set this
straight in our minds, consider the following example. In general, the same
reasoning shows that there are

different permutations of *n* objects, of which *n*_{1} are alike, *n*_{2} are
alike, ..., are alike.

**Example**- How many different letter arrangements can be formed using the letters
?*P E P P E R*

*Solution:*- We first note that there are 6! permutations of the letters
*P*_{1}*E*_{1}*P*_{2}*P*_{3}*E*_{2}*R*when the 3's and the 2*P*'s are distinguished from each other. However, consider any one of these permutations -- for instance,*E**P*_{1}*E*_{1}*P*_{2}*P*_{3}*E*_{2}*R*. If we now permute the's among themselves and the*P*'s among themselves, then the resultant arrangement would still be of the form*E*. That is, all 3!2! permutations*P E P P E R*are of the form

. Hence there are possible letter arrangements of the letters*P E P P E R*.*P E P P E R*