Question

Show mathematically why we take 0! to be = 1.

Answer 1

0=1 in application to what?

Answer 2

I mean factorial 0. factorial 4 = 4! = 4*3*2*1

Answer 3

now let us consider the experiment of drawing 3 balls from the given set of 3 balls... we know we can do it in 1 way. or 3C3, for now let us consider 0!=k some real non-zero value.
we know, 3C3=3!/(0!3!)=1/k. but we know that the number of ways is 1 and hence k has to be 1.
therefore... 0!=1.

Answer 4

Mathematically, \(\dfrac{n!}{n} = (n - 1)!.\) This implies that \(\dfrac{1!}{1} = 1 = (1 - 1)! = 0!\)