n！ =n*(n- 1)！

1! = 1

1! = 1*0!

If 0! =0, then 1! = 1*0! =0, and 1! Contradictions, and can deduce the wrong result that all factorials are 0. So, the rule is 0! = 1。

Factorial represents complete permutation, and its essence is permutation and combination. The total number of all the ways to take n from n is now 0! , that is, take out 0 from 0, naturally choose this method, so 0! = 1, but you don't have to worry so much, just remember the math rule 0! = 1 will do.

Factorial number and total permutation;

The so-called factorial number means that the base of its lowest bit is 1, that is, every one goes in, and every one goes higher, that is, the carry is two, three, and the n-bit factorial number * * has n! A. For example, the three factorials are 000, 0 10, 100,1/kloc-0, 200, 2 10. Let n-ary set S={a 0, a 1, a2, … an- 1}, then the complete permutation of s corresponds to the factorial number of n bits one by one.

The corresponding way is: there are n ways to choose the first element from n elements. The subscript value of the selected element is an integer between 0 and n- 1, which is the highest digit of the factorial number of n, and the other elements are renumbered from 0 to n-2 according to the subscript, and their relative order is not changed when renumbering.