In Mathematics, permutation is an important concept used to calculate the way elements in a given set are combined. Here are some relevant tips about permutations:

1. Definition of permutation: a permutation is an ordered arrangement of a specified number of elements from a given finite number of distinct elements. The formula for permutation is A(n,m)=n!/(n-m)! , where n denotes the total number of elements, m denotes the number of elements to be removed, and "!" denotes the factorial operation.

2. Definition of Combination : Combination is the unordered arrangement of a specified number of elements from a given finite number of distinct elements. The formula for combination is C(n,m)=n!/[m!*(n-m)! , where n represents the total number of elements, m represents the number of elements to be removed, and "!" denotes the factorial operation.

3. Tips for using combinatorial formulas: when it is necessary to calculate the number of combinations of r elements to be taken out of n different elements, you can use the combinatorial formula C(n,r)=n!/[r!*(n-r)!!!] . This formula simplifies the calculation process, especially when n and r are large.

4. Tips for using the permutation formula: when it is necessary to calculate the number of permutations of r elements from n different elements in an orderly arrangement, you can use the permutation formula A(n,r)=n!/(n-r)! This formula also simplifies the calculation process, especially when n and r are large.

5. Elimination: in some complex combinations of problems, can be eliminated to simplify the calculation process. The basic idea of elimination is to exclude from the total number of cases that do not meet the conditions, so as to obtain the final result.

6. Recursive relationship: for some of the recursive relationship of the permutation and combination of problems, 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 computation.

7. Generating function method: for some complex permutation problems, you can use the generating function method to solve. Generating function is a way to transform the permutation problem into an algebraic equation, through the generating function of the derivative, expansion and other operations, you can get the final result.

8. Use of symmetry: In some permutation problems with symmetry, symmetry can be used to simplify the calculation process. By observing the symmetry of the problem, it can be realized that the order of certain elements does not affect the final result, thus reducing the amount of computation.