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# Why zero factorial is 1 ?please explain with proof ....Thanks...

Aman Bansal
592 Points
9 years ago

Dear HAsan,

If n! is defined as the product of all positive integers from 1 to n, then:
1! = 1*1 = 1
2! = 1*2 = 2
3! = 1*2*3 = 6
4! = 1*2*3*4 = 24
...
n! = 1*2*3*...*(n-2)*(n-1)*n
and so on.
Logically, n! can also be expressed n*(n-1)! .

Therefore, at n=1, using n! = n*(n-1)!
1! = 1*0!
which simplifies to 1 = 0!

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Pulkit Singhal
25 Points
9 years ago

nPr=  n! / (n-r)!

put r=n

nPn = n! / (n-n)!

n! = n! / 0!

0! = n! / n!

0! = 1

Proved