Home > Common Problem > body text

What are the commonly used permutation and combination formulas?

小老鼠
Release: 2023-10-24 11:16:19
Original
24995 people have browsed it

Commonly used formulas include permutation formulas, combination formulas, repeated permutation formulas, repeated combination formulas, etc. Detailed introduction: 1. Arrangement formula: The number of ways to select m elements from n elements for arrangement: P(n, m) = n! / (n - m)!, The number of full arrangement methods for n elements: P (n, n) = n!; 2. Combination formula: Number of ways to select m elements from n elements for combination: C(n, m) = n! / (m! * (n - m)!) etc.

What are the commonly used permutation and combination formulas?

In permutation and combination, commonly used formulas include:

  1. Permutation formula:

    • The number of ways to select m elements from n elements for arrangement: P(n, m) = n! / (n - m)!
    • The number of full arrangement methods for n elements: P( n, n) = n!
  2. Combination formula:

    • Number of ways to select m elements from n elements for combination: C (n, m) = n! / (m! * (n - m)!)
    • The number of ways to select m elements from n elements for combination (simplified form): C(n, m ) = C(n, n-m)
  3. Repeated arrangement formula:

    • The number of ways to repeatedly select m elements among n elements for arrangement :P'(n, m) = n^m
  4. Repeated combination formula:

    • Repeatedly select m elements among n elements. Number of combination methods: C'(n, m) = C(n m - 1, m)

These formulas are very useful when calculating permutation and combination problems and can help determine The total number of options and arrangements of elements. It should be noted that the premise of these formulas is that elements cannot be selected repeatedly. If elements are allowed to be selected repeatedly, repeated arrangement and repeated combination formulas need to be used.

The above is the detailed content of What are the commonly used permutation and combination formulas?. For more information, please follow other related articles on the PHP Chinese website!

source:php.cn
Statement of this Website
The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn
Popular Tutorials
More>
Latest Downloads
More>
Web Effects
Website Source Code
Website Materials
Front End Template
About us Disclaimer Sitemap
php.cn:Public welfare online PHP training,Help PHP learners grow quickly!