The arrangement number is to take any m(m≤n) elements from n different elements (the elements taken out are different) and arrange them in a certain order, which is called the arrangement of taking out m elements from n different elements.

The combination number refers to taking any m(m≤n) elements from n different elements to form a group, which is called taking m elements from n different elements; The number of all combinations of m(m≤n) elements from n different elements is called the number of combinations of m elements from n different elements. Represented by the symbol c(m, n).

For example, choose 5 letters from 26 letters.

Arrangement: A (A(26,5) means to arrange five letters in a line from 26 letters; That is, ABCDE is different from brominated diphenyl ethers and brominated diphenyl ethers.

Combination: C(26, 5) means that there is no order in choosing five of the 26 letters; In other words, ABCDE is equivalent to ACBDE and ADBCE.

Step 2 calculate

(1) permutation number formula

This arrangement is represented by symbols A(n, m) and m _ n.

The formula is: a (n, m) = n (n-1) (n-2) (n-m+1) = n! /(n-m)！

Besides, the rule is 0! = 1，n！ Represents n(n- 1)(n-2)? 1

For example: 6! =6x5x4x3x2x 1=720，4！ =4x3x2x 1=24 .

(2) Combination number formula

This combination is represented by symbols C(n, m) and m _ n.

The formula is: C(n, m)=A(n, m)/m! Or C(n, m)=C(n, n-m).

For example: c (5,2) = a (5,2)/[2! x(5-2)！ ]=( 1x 2 x3 x4 x 5)/[2x( 1x2x 3)]= 10 .

Extended data:

There are two definitions of arrangement, but there is only one calculation method, and those who meet these two definitions are calculated in this way; The premise of the definition is that m_n, m and n are natural numbers.

(1) Arranging any M elements in a certain order from N different elements is called taking out the arrangement of M elements from N different elements.

(2) Taking out all the arrangements of M elements from N different elements is called taking out the arrangements of M elements from N different elements.

Permutation and combination is the most basic concept of combinatorics. The so-called arrangement refers to taking out a specified number of elements from a given number of elements for sorting. Combination refers to taking out only a specified number of elements from a given number of elements, regardless of sorting.

The central problem of permutation and combination is to study the total number of possible situations in a given permutation and combination. Permutation and combination are closely related to classical probability theory.

References:

Baidu Encyclopedia Entry-Combination Number Formula