Let us suppose a finite set A is given. The permutation of the elements of set A is any sequence that can be formed from its elements.

If all the elements of set A are not different, the result obtained are permutations with repetition.

If set A which contains n elements consists of n₁ elements of the first kind, n₂ elements of the second kind,..., and n_k elements of k-th kind (n=n₁+n₂+...+n_k), the number of permutations with repetition is given by:

In general, repetitions are taken care of by dividing the permutation by the number of objects that are identical! (factorial). 

How many different 5-letter words can be formed from the word DEFINITION?

       _10!_   =   3628800    =    302400 words
        2!·3!           12

You divide by  2! because the letter N repeats twice.
You divide by  3! because the letter I repeats three times.

Enter the number of elements of the set A and the number of different elements and the computer will calculate you how many permutations without repetition of the elements are there?

Number of different elements