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.
The definition of permutation and its calculation formula;
From n different elements, any M (m ≤ n, m and n are natural numbers, the same below) elements are arranged in a column in a certain order, which is called the arrangement of taking out m elements from n different elements; All permutation numbers of m(m≤n) elements taken from n different elements are called permutation numbers of m elements taken from n different elements, which are represented by symbol A(n, m).
A(n，m)= n(n- 1)(n-2)……(n-m+ 1)= n！ /(n-m)！
Besides, the rule is 0! = 1。 Where n! Represents factorial, that is, n! =n(n- 1)(n-2)... 1
Definition and calculation formula of combination;
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. Represented by the symbol C(n, m).
C(n，m)=A(n，m)/m！
C(n，m)=C(n，n-m)