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# Permutations with repetition

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 nk elements of k-th kind (n=n1+n2+...+nk), 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?

$\frac{10\cdot9\cdot8\cdot7\cdot6}{3!\cdot2!}$  =    2520 words

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