why 0!=1??

Answer 1

just to clarify the last answer ... you can generalise n! to a function of any real argument .. gamma(x) where gamma(x+1) = x! when x is an integer... in fact gamma(x) = (x-1) gamma(x-1) is a defining property.

when you look at the gamma function, the limit as x ->1 is 1, and its CONVENIENT therefore to take gamma(1) = 0! = 1

Answer 2

This comes from the generalization through calculus of the "factorial function" as an integral of a certain function of x and n . This integrand function will yield 0! = 1 for n = 0

For better details look up Gamma function

Answer 3

LETS START WITH AN EXAMPLE:

NUMBER OF WAYS OF ARRANGING THE DISTINCT LETTERS OF A WORD(WITHOUT REPETITION) WITH 'N' CHARACTERS?

(EG) WORD: 123
123
231
312
132
312
213

ie. N! WAYS

NUMBER OF WAYS OF ARRANGING THE DISTINCT LETTERS OF A WORD(WITHOUT REPETITION) WITH 1 CHARACTER?

OBVIOUSLY 1! WAYS

NUMBER OF WAYS OF ARRANGING THE DISTINCT LETTERS OF A WORD(WITHOUT REPETITION) WITH 0 CHARACTERS?

IT IS SAME AS TAKING N BALLS FROM A BASKET WHICH CONTAINS N BALLS...

OBVIOUSLY YOU HAVE ONLY ONE CHOICE... CHOOSE ALL OF THEM... (ONLY ONE WAY)

IN THIS CASE YOU HAVE ONLY ONE ARRANGEMENT IN THAT WORD... THE WORD ITSELF AS IN THE CASE OF 1 CHARACTER WORD...

SO,
0!=1!=1