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A stands for arrangement, which means that a specified number of elements are taken out from a given number of elements for sorting.
Arrangement is to arrange each element in a certain order and calculate the number of arranged elements. The basic idea of permutation is to regard the n elements to be taken out as being placed in a row, and all permutation numbers of m elements are taken out from these n elements.
combine
C stands for combination, which means that only a specified number of elements are taken out of a given number of elements regardless of the sorting.
Combination is all ways to take out m elements from n different elements, regardless of the order in which the elements are taken out. Therefore, in arrangement, order is very important, but in combination, order is not important. So when arranging or combining questions, you need to decide whether to use A or C according to the requirements of the questions.
Application of permutation and combination
combinatorial mathematics
Combinatorial mathematics is a branch of mathematics that studies combinatorial problems, such as combinatorial counting and combinatorial optimization. Combinatorial mathematics is widely used in computer science, information theory, operational research and other fields. For example, in computer science, combinatorial counting can be used to solve problems such as finding all possible solutions in a given time.
probability theory
Permutation and combination also have important applications in probability theory. For example, when calculating probability distribution, confidence interval and hypothesis test, it is necessary to arrange and combine to calculate the number of possible results.
statistics
In statistics, permutation and combination are used to calculate various statistics, such as mean, median and variance. In addition, permutation and combination are also used for fitting statistical models, hypothesis testing and regression analysis.
operational research
Operational research is a discipline that studies and optimizes the allocation of resources. In operational research, permutation and combination are used to solve problems such as task allocation and resource scheduling. For example, in task assignment, you can use permutation and combination to calculate all possible assignment methods and choose the best one.