From n different elements, any m(m≤n) elements are arranged in a column in a certain order, which is called the arrangement of m elements in n different elements; All permutation numbers of m(m≤n) elements from n different elements are called permutation numbers of m elements from n different elements, which are represented by the symbol p(n, m).

p(n，m)= n(n- 1)(n-2)……(n-m+ 1)= n！ /(n-m)！ (regulation 0! = 1).

2. Combination and calculation formula

Taking out any m(m≤n) elements from N different elements and grouping them is called taking out the combination of 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. Use symbols.

C(n, m) represents.

c(n，m)=p(n，m)/m！ =n！ /((n-m)！ *m！ ); c(n，m)=c(n，n-m)；

3. Other permutation and combination formulas

Cyclic permutation number of r elements in n elements = p (n, r)/r = n! /r(n-r)！ .

N elements are divided into K classes, and the number of each class is n 1, n2, ... nk. The total arrangement number of these n elements is

n！ /(n 1！ *n2！ *...*nk！ ).

K-type elements, the number of each class is infinite, and the combined number of M elements is c(m+k- 1, m).

Arrangement (Pnm(n is subscript, m is superscript))

Pnm=n×(n- 1)....(n-m+ 1)； Pnm=n！ /(n-m)！ (Note:! Is a factorial symbol); Pnn (two N's are superscript and subscript respectively) =n! ; 0! = 1; Pn 1(n is subscript 1 is superscript) =n

Combination (Cnm(n is subscript, m is superscript))

CNM = Pnm/Pmm； Cnm=n！ /m！ (n-m)！ ; Cnn (two n's are superscript and subscript respectively) =1; Cn 1(n is subscript 1 is superscript) = n；; Cnn = Cnn-m