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 Factorial Variations without repetition Variations with repetition Permutations with repetition Permutations without repetition Exercises Circular permutations Binomial coefficient Combinations with repetition Combinations without repetition
 Arithmetic mean

 Combinatorics 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         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