Suppose we want to choose m people from n people to arrange.

therefore

The first position has n options;

Choose n-1for the second position-because one person was chosen for the first position, only n-1was chosen here;

The third position is selected from n-2;

……

The m position is selected from N-M+ 1.

These choices are progressive (step by step), so we use multiplication to calculate, so there is always n * (n-1) * (n-2) ... * (n-m+1), in which a * * * has m terms.

We define this formula as:

P (n, m) = n * (n-1) * (n-2) ... * (n-m+1) means that m samples are selected from n populations for arrangement.

Especially when M=N, we call it total permutation, and define P(N, N)=N! = n * (n-1) * (n-2) * ... * 2 *1and p (0,0) = 0! = 1

I hope it helps you.