Permutation and combination formulas/permutation and combination calculation formulas

Common permutation and combination formulas:

Formula p Refers to the arrangement, where n elements are sorted by R.
Formula C refers to a combination, where R elements are obtained from n elements without arrangement.
Total number of N-Elements
Number of elements involved in the selection by R
! -Factorial, for example, 9! = 9*8*7*6*5*4*3*2*1

From n to R, the expression should be n * (n-1) * (n-2)... (n-R + 1 );

Because the number from N to (n-R + 1) is N-(N-R + 1) = r

Example:

Q1: there are 9 Number balls in total from 1 to 9. How many three digits can be made up?

A1: 123 and 213 are two different numbers. That is, those who have requirements on the order of arrangement belong to the scope of "arrangement P" calculation.

In the above problem, any number can only be used once. Obviously, there will be no combinations such as 988,997. We can see that there are 9 possibilities for hundreds of BITs, and 9-1 for dozens of bits, the number of single digits must be 9-1-1, with a total of 9*8*7 three digits. Formula = P (3, 9) = 9*8*7, (product of the last three from 9)

Q2: there are 9 football balls ranging from 1 to 9. How many "Three Kingdoms alliance" Can a group of three representing the "Three Kingdoms alliance" be combined "?

A2: A combination of 213 and 312 represents the same combination, as long as there are three number balls together. That is, the order is not required and belongs to the "combined C" Computing category.

In the above problem, remove all the numbers including the number of permutation numbers that belong to duplicates, that is, the final combination number C (7/3) = 9*8*2*1