There are two definitions of arrangement, but there is only one calculation method. Those who meet these two definitions are calculated in this way. The premise of the definition is that m≤n, and both m and n are natural numbers. The calculation method and formula of permutation and combination C are introduced below for reference.

How to calculate a and c in permutation and combination? The arrangement A (n, m) = n× (n- 1). (n-m+ 1) = n！ /(n-m)！ (n is subscript and m is superscript, the same below)

Combination C(n, m)=P(n, m)/P(m, m)=n! /m！ (n-m)！ ;

For example, a (4,2) = 4! /2! =4*3= 12

C(4，2)=4！ /(2! *2! )=4*3/(2* 1)=6

A32 is permutation, C32 is combination.

For example, A32 is 3 times 2 equals 6.

A63 is 6*5*4.

That is, starting from a big number and multiplying by a later number indicates how many numbers there are. A72 equals 7*6*2, so there are two numbers A52=5*4.

Then C32 is divided by a number, for example, C32 is A32 and then divided by A22.

C53 is A53 divided by A33.

There are two definitions of combination and its calculation formula combination. The premise of the definition is m ≤ n.

(1) Taking any M elements from N different elements to form a group is called taking the combination of M elements from N different elements.

② The number of all combinations of M elements of N different elements is called the number of combinations of M elements of N different elements.

③ Understand the definition with examples: How many combinations can two colors form from four colors?

Solution: c (4,2) = a (4,2)/2! = {[4x(4- 1)x(4-2)x(4-3)x(4-4+ 1)]

[Calculation formula]

This combination is represented by the symbol C(n, m), 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 .