1. Combinatorial mathematics: permutation method is the basis of combinatorial mathematics, which is used to calculate all possible combinations of m elements from n different elements. For example, what is the number of combinations of three people selected from 10?
2. Probability theory: permutation method is also widely used in probability theory to calculate the probability of events. For example, how many possible ways are there to randomly draw 5 cards from a deck of 52 cards?
3. Cryptography: permutation method also has important applications in cryptography to generate and crack passwords. For example, Caesar password is a simple replacement password based on permutation.
4. Statistics: In statistics, the arrangement method is used to calculate the size of the sample space and calculate the differences between multiple samples. For example, suppose there are five different products, and each product has three different colors. How many possible color combinations are there?
5. Computer science: permutation method is also widely used to solve search problems and graph theory problems in computer science. For example, Traveling Salesman Problem (TSP) is a classic problem solved by permutation method.
6. Economics: In economics, problems such as consumer choice and production plan are analyzed by permutation method. For example, suppose a consumer has three commodities to choose from, and each commodity has two brands to choose from. How many possible consumption combinations are there?