why is factorial of 0 , '1'?

Answer 1

It is assumed so to overcome some situations.
According to theory of p[ermutation arrangment of 'n' objects canbe done in n! ways. Suppose we have 10 objects. Number of
ways of arranging no objects can be done only in one way(dont arrange)
Using permutation, no:=0! which is equal to 1 by meaning

Answer 2

the factorial of 1 is 1. the factorial of 0 is 1.

Answer 3

Well, you can't figure it from first principles, but you do need 0! to equal 1 to be consistent with the definitions.
Let's work backward from 3!:

3!=2!x3=6

2!=1!x2=2

1!=0! x 1 = 1

Look at that last equation: 1 times something (0!) equals 1. So what does that something (0!) have to be? One (exclamation point, not factorial sign here).

Answer 4

its 0

Answer 5

In math, never accept answers like "because it's defined that way." Math has to make sense and all hang together. Things like 0! aren't just defined to make things convenient. They are derived.

There is a function called the Gamma function that extends the notion of factorials to numbers besides the integers. Related to the Gamma function is the integral equality:

(Integration from t=0 to infinity)(e^(-t)*t^n*dt) = n!

This function requires multiple integrations by parts to be evaluated but it does evaluate to n! for all positive integers. For the case n=0 it evaluates to 1. Since the function works for all positive integers, the value it returns for n=0 must be right as well. This defines 0! = 1.

For what its worth, the factorial of any negative integer is undefined and this integral shows that as well.

Answer 6

It is a convention; 0! is defined as 1. The reasons are mathematical:

The recursive definition of a factorial, (n + 1)! = n! × (n + 1) works for n = 0;

This definition makes many identities in combinatorics valid for zero sizes. In particular, the number of arrangments or permutations of an empty set is just one

Answer 7

we can see the sequence here...
4! = 5!/5 = 120/5 = 24.
3! = 4!/4 = 24/4 = 6
2! = 3!/3 = 6/3 = 2
1! = 2!/2 = 2/2 = 1
0! = 1!/1 = 1/1 = 1
The sequence gives 0!=1

Answer 8

e = 1/0! + 1/1! + 1/2! + 1/3! + ... .
If you define 0! = 1! = 1 then e is really 2.71828...,
the base of the natural logarithm.

Th

Answer 9

0! = 1 and 1! = 1. for prove refer any good text maths

Answer 10

We know that,
1! =1
or, 1(1-1)!=1 since,n! = n(n-1)!
or, 1.0!=1
or, 0!=1.