Definition of 1. Arrangement: Arrangement refers to taking out a specified number of elements from a given limited number of different elements for orderly arrangement. The calculation formula of permutation is A(n, m)=n! /(n-m)！ , where n represents the total number of elements and m represents the number of elements to be taken out, "!" Represents a factorial operation.
2. Definition of combination: combination refers to taking out a specified number of elements from a given limited number of different elements for disorderly arrangement. The formula of combination is C(n, m)=n! /[m！ *(n-m)！ ], where n represents the total number of elements and m represents the number of elements to be taken out, "!" Represents a factorial operation.
3. Skills of using the combination formula: When it is necessary to calculate the combination number of R elements from N different elements, you can use the combination formula C(n, r)=n! /[r！ *(n-r)！ ]。 This formula can simplify the calculation process, especially when n and r are large.
4. Skills of using the arrangement formula: When you need to calculate the arrangement number of R elements from N different elements for orderly arrangement, you can use the arrangement formula A(n, r)=n! /(n-r)！ . This formula can also simplify the calculation process, especially when n and r are large.
5. Exclusion method: In some complex permutation and combination problems, exclusion method can be used to simplify the calculation process. The basic idea of exclusion method is to exclude unqualified cases from the total situation, so as to get the final result.
6. Recursive relation: For some permutation and combination problems with recursive relation, recursive relation can be used to simplify the calculation process. By finding the recurrence relation of the problem, the problem can be decomposed into smaller sub-problems, thus reducing the amount of calculation.
7. Generation function method: For some complex permutation and combination problems, the generation function method can be used to solve them. Generating function is a method to transform permutation and combination problem into algebraic equation. The final result can be obtained by derivation and expansion of the generating function.
8. Using symmetry: In some symmetric permutation and combination problems, symmetry can be used to simplify the calculation process. By observing the symmetry of the problem, we can find that the order of some elements does not affect the final result, thus reducing the amount of calculation.