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单词 permutation
释义

permutation

In combinatorics, a permutation of n objects is an arrangement n objects. The number of permutations of n objects is equal to n!. The number of ‘permutations of r objects from n objects' is denoted by nPr, and equals

For example, there are 12 permutations of A, B, C, D taken two at a time: AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC.

Suppose that n objects are of k different kinds, with r1 alike of one kind, r2 of a second kind, and so on. Then the number of distinct permutations of the n objects equals the multinomial coefficient

where r1 + r2 + … + rk = n. For example, the number of different anagrams of the word ‘CHEESES' is 7!/3! 2!, which equals 420. Compare combination.

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更新时间:2025/5/21 0:48:07