How to solve the permutation and combination problem Explain it in detail

The formula for calculating the combination of the chop and the row:Permutation a(n,m) = n (n-1). （n-m+1）=n!/（n-m）!(n is the subscript, m is the superscript, the same below).

Combination c(n,m) = p(n,m) p(m,m) =n!/m!（n-m）!

For example, the spring rolling car:

a(4，2)=4!/2!=4*3=12

c(4，2)=4!/(2!*2!)=4*3/(2*1)=6Division1. Divide by a number that is not equal to zero, which is equal to the reciprocal of multiplying this number.

2. Divide the two numbers, the same number is positive, the different number is negative, and divide the absolute value of the quarrel. Zero divided by any number that is not equal to zero gives zero.

Note: Zero cannot be a divisor and denominator.

Division and multiplication of rational numbers are inverse operations.

Solution: cnm = anm amm, where the permutation number (also known as the number of optional permutations) is stupidly used as the representation of anm and the full permutation number ann.

Multiplication means: anm=n(n-1)(n-2).n-m+1)。

The factorial denotes: anm=n!/(n-m)!

The calculation method for the combination of the rows and columns is as follows:

Permutation a(n,m) = n (n-1). （n-m+1）=n!/（n-m）!(n is the subscript, m is the superscript, and the same is the same as the file bureau).

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。

Division is done to remove duplicates.

I'll show you how to do it, if there are 4 symbols 4, a, b, and c to be fully arranged once, the answer is p4

Name it out. 4abc,4acb,4bac,4bca,4cab,4cba;

a4bc,4acb,b4ac,b4ca,c4ab,c4ba;

ab4c,ac4b,ba4c,bc4a,ca4b,cb4a;

abc4,acb4,bac4,bca4,cab4,cba4;

Now you are asked to ignore the order of the ABCs, or how do you rank them if the ABCs are all the same number?

You will find that the first row listed belongs to the same situation, and the second row is in the same situation.

You ignore the 4 in each row above, and each row of them is the full arrangement of abc p3, so just p4 p3 is fine.

The meaning of division here is that when the permutation P3 of ABC is considered to be the same case, it is removed from the total.

You can come up with a super simple problem on scratch paper that mimics your workbook and try to solve it in your own way. Count it by example. In fact, if the same amount of grouping is not removed, it will be repeated.

As for why the team is divided first and then arranged, that's a routine. Do more questions, look at the detailed answer process, and you will understand.

You'll have to come up with a specific permutation so that we can explain it to you.