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
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Junior high school mathematics formula: permutation and combination formula
Junior high school mathematics formula: permutation and combination formula
The senior high school entrance examination network has compiled the formula of junior high school mathematics: permutation and combination formula, hoping to be helpful to the students and for reference only.
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