Why 0!= 1 in Mathematics?

this is in probabilite

(we have n(n-1)(n-2).......(n-n+1)=A(n,n                  

             =1*2............(n(n-1)(n-2

(and n!/0!=A(n,n

finaly 0!=1

To calculate the probabilities , and n!=(n+1)! / (n+1) .... It's simple.

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 n! = n*(n-1)!

n= 1

 

1! = 1*0!1 = 0!