Question

How can we derive that 0!=1.???

Answer 1

We cant derive that 0!=1
But we can see that 0!=$\frac{1!}{1}$
Which equals to 1

Answer 2

To Prove:- 0! =1.
Known:y! = y x (y-1)!
So, 1! = 1 x (1-1)!1! = 0! 
or 
0! = 1! -(a)
Proof:As We know,n! = n x n-1 x n-2 x n-3 x n-4 x .......... 2 x 1
So,4! = (3+1)!
 = 4 x 3!
= 4 x 3 x 2 x 13!
= (2+1)!
= 3 x 2!
= 3 x 2 x 1 2!
= (1+1)!
= 2 x 1!
= 2 x 11!
= (0+1)!
= 1 x 0! = 1 -(b)
Hence, from (a) and (b)We get, 0! = 1