Mathematics - Combinatorial Analysis - Permutation involving repeated elements

We understand permutation an ordered sequence, built by available elements. The number of permutations of n elements It is given by n factorial that is just calculate the factorial of the number of elements from the set. For a better understanding we will consider the DOG word anagram. Recalling that anagram of a word corresponds to the permutation of letters in a word, forming or not another word. Watch: 

In the case of the word DOG, there is no repetition of letters, then we can determine the anagrams using the following mathematical expression:   Pn = n!

 P3 = 3! = 3*2*1 = 6

 The word Dog has 6 anagrams. 

Permutation involving a repeated element

Determine the anagrams of the word Puzzles.

The anagrams are formed from a sequence of letters 7, two of which are equal to Z. 

This way we have: 

Permutation involving two different elements repeated

Determine the anagrams of the word Quizzing.

Anagrams will be formed from the following eight letters, two of which are equal to I and two equal to Z. 

We have: 

Other situations involving repeated elements

Anagrams of the word Crackbacks.

In this case we have 10 letters, where the following repetitions occur: two letters A, three letters C and two letters K. 

Then: