Think about solving problems:

The algorithm of 4 under the mathematical symbol C and 2 above belongs to the solution of combined formula.

1, according to the combination formula

C(4，2)=4！ /2! (4-2)!

2, molecule: 4!

Denominator: 2! (4-2)!

4! It means factorial of 4, 4! =4*3*2* 1=24, others are the same as 2! =2* 1=2

(4-2)! =2! =2* 1=2

3, denominator 2! (4-2)! =2*2=4

4、C(4，2)=4！ /2! (4-2)! =24/4=6

Combination definition

Combination is one of the important concepts in mathematics. Taking out M different elements (0≤m≤n) from N different elements at a time and synthesizing a group regardless of their order is called selecting the combination of M elements from N elements without repetition. The total number of all such combinations is called the combination number, and the calculation formula of this combination number is

or

The combination obtained by repeatedly extracting m elements from the n-ary set A is essentially an m-ary subset of A ... if you sort the first set. To be an ordered set, how many segments does the combination of m elements extracted from A correspond to? A definite strict order-preserving mapping to ordered set A, the number of combinations? Commonly used symbols are

C stands for combination. If the subscript is n, multiply it by n (n- 1)(n-2)(n-3) ... How much do you need to multiply it? Look at the superscript, the superscript is 2, so a * * * needs to be multiplied by two numbers, which is n(n- 1), so we get 4X3. For example, C (6,3), superscript 3, starting with subscript 6 times 3, the number 6X5X4.

We're halfway through this step, and we're going to divide the above result by a number. Assuming that the superscript is m, we will use m(m- 1)(m-2)(m-3) ... until the final number is 1. For example, if the superscript is 4, the divisor is 4X3X2X 1=24, the superscript is 6, and the dividend is 6X5X4X3X2X 1=720.

Finally, the result of the first step divided by the result of the second step is equal to the operation result 6 of c (4,2).

It seems that there are many language descriptions. As long as you understand what I said, the actual operation is very simple.

Supplement:

Arrangement:

A(4，2)=4X3

A(6，6)=6X5X4X3X2X 1

4 is the foot code below, 2 is the number above, the number below represents multiplication from this number, and the number above represents a * * *, multiplied by how many numbers. The law of multiplication is that the number behind is less than the number before 1.

Combination:

C(4，2)=(4X3)/(2X 1)

C(6，6)=(6x 5x 4 x 3x 2x 1)/(6x 5x 4 x 3x 2x 1)

The first step of the combination algorithm is exactly the same as the arrangement. One step beyond the arrangement is to divide by a number, and the divided number is the product of the above number multiplied by 1.