1, arrangement

The subsets of finite sets are arranged in columns and are circular, and they are not allowed to be repeated or repeated according to some conditional sorting method.

Take out m( 1≤m≤n) different elements from n different elements at a time and arrange them in a row, which is called non-repetitive arrangement or linear arrangement of taking out m elements from n elements, which is called arrangement for short.

Note: Two permutations are the same if and only if the elements are exactly the same, and the arrangement order of the elements is the same.

2. Combination

Taking out M different elements (0≤m≤n) from N different elements at a time and synthesizing a group regardless of their order is called selecting the combination of M elements from N elements without repetition.

The total number of all these combinations is called the combination number, and the calculation formula of this combination number is:

or

The combination obtained by repeatedly extracting M elements from N-ary set A is essentially an M-ary subset of A. ..

Extended data:

Common methods of permutation and combination:

First, the adjacent topic binding method.

Adjacent refers to multiple adjacent elements; Binding is to treat adjacent elements as a whole.

Secondly, the interpolation method of phase separation problem.

Separate, that is, not adjacent, insert other elements in non-adjacent elements.

Thirdly, the reduction method of scheduling problem.

Sorting is to keep several elements in a certain order, and it is more convenient to solve this kind of problem by reducing the multiple.

Fourthly, the step-by-step method of label sorting problem.

Five, the demand distribution problem points.

Sixth, the classification of multivariate problems.

Seven, cross problem set method.

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