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?
_10!_ = 3628800 = 302400 words
You divide by 2! because the letter N repeats twice.
You divide by 3! because the letter I repeats three times.