Why factorial of zero is equals to one not zero - 0! = 1 ?

byAmlesh Mahato •

Factorial is a mathematical operator. If we take factorial of 5 then its equal to 5x4x3x2x1. Factorial is represented by ! or ㄴ. If n is the number then factorial of n can be represented by n! or ।n.

Why factorial of zero is equals to one not zero - 0! = 1 ?, What is a factorial of 0? Can you have 0 factorial? Is 0 factorial undefined? What is the value of factorial?, factorial of one why factorial of 0! is 1 factorial of 0 proof what is 0! 0!=1 proof 0 = 1 why 0 factorial is 1? - quora factorial of negative number
Why factorial of zero is equals to one not zero - 0! = 1 ?

  Follow Us  

For example:

2! = 2x1

3! = 3x2x1

4! = 4x3x2x1

5! = 5x4x3x2x1

n! = nx(n-1)x(n-2)x(n-3)x.............

From above now we have a basic idea about factorial. We have a got a chapter called Permutation and Combination in class 10, 11 and 12 mathematics or advance mathematics.

⇒From that chapter we know, When r ≤ n then
nPr=
n! / (n-r)!
⇒Now when r = 1
nP1=
n! / (n-1)!
=
n(n-1)! / (n-1)!
=n
⇒Now when r = 2
nP2=
n! / (n-2)!
=
n(n-1)(n-2)! / (n-2)!
=nx(n-1)
⇒Now when r = 3
nP3=
n! / (n-3)!
=
n(n-1)(n-2)(n-3)! / (n-3)!
=nx(n-1)x(n-2)

⇒From above we can conclude that

nP1=n
nP2=nx(n-1)
nP3=nx(n-1)x(n-2)
nPn=nx(n-1)x(n-2)x(n-3)x........=n!
nPn=n!
⇒
n! / (n-r)!
=n!
⇒
n! / (n-n)!
=n!
⇒
n! / 0!
=n!
⇒0!=
n! / n!
⇒0!=1
That is why factorial of zero is equal to one note zero i.e. 0! = 1 is true.
Tags:
Previous Post Next Post