I. Algorithm

P(n，m) = n！ / (n-m)！

Where, n! Represents the factorial of n, that is, n×(n- 1)×n...× 1.

n-m)！ Represents the factorial of (n-m).

For example, p (5,3) is the permutation number of three of the five elements.

We can use the formula of permutation number to calculate: p (5,3) = 5! / (5-3)!

The calculation result is: p (5,3) = 60.

Second, the concept

The formula of permutation number is to randomly select m(m≤n) elements from n different elements (the extracted elements are different) and arrange them in a certain order, which is called the arrangement of m elements in n different elements. Arrangement is related to the order of elements, and combination has nothing to do with order. Addition principle sum multiplication principle is the basis of permutation and combination.

All permutation numbers of m(m≤n) elements from n different elements are called permutation numbers of m(m≤n) elements from n different elements. Marked as am/n, a is the first capital letter of English arrangement.

Third, symbols

C: number of combinations

Answer: Number of permutations (P in old textbooks)

N: the total number of elements

M: the number of elements participating in the selection

! Factorial, such as 5! =5×4×3×2× 1= 120

C: combination combination

P: permutation arrangement (now the textbook is A arrangement)

Application of permutation number algorithm

First, combinatorial mathematics.

The permutation number and combination number are the basis of combinatorial mathematics, which describes the number of all possible combinations or permutations of m elements from n different elements. These numbers are basic counting tools in combinatorial mathematics, which are widely used in combinatorial analysis, probability theory, statistics and other fields.

Second, probability theory.

The permutation number also has important applications in probability theory. For example, when calculating some probability distributions, we need to calculate the arrangement number of m elements from n elements to determine the probability of some events.

Third, statistics.

In statistics, permutation number is used to calculate the distribution of some statistics. For example, when calculating the degree of freedom of chi-square test, we need to calculate the arrangement number of k observations from n observations.

Fourth, computer science.

Rank numbers are also widely used in computer science. For example, in the analysis and design of algorithms, we need to calculate the arrangement number of M elements from N elements to determine the spatial complexity of some algorithms.

Verb (abbreviation of verb) physics

In physics, permutation numbers are also used to calculate some physical quantities. For example, in quantum mechanics, we often need to calculate the arrangement number of some quantum states to determine the distribution of some physical quantities.