Current location - Training Enrollment Network - Mathematics courses - Kneel for all calculation methods and formulas of high school mathematics permutation, combination and probability. ..
Kneel for all calculation methods and formulas of high school mathematics permutation, combination and probability. ..
1. Arrangement and calculation formula

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