A factorial is the product of an integer and all the integers below it i.e. factorial four ( *4!* ) is equal to 24 (= 4 x 3 x 2 x 1) But if this is so, why is 0! = 1, because technically, 0! = 0 x 0 right? So WHY??

If n! is defined as the product of all positive integers from 1 to n, then:

1! = 1 x 1 = 1

2! = 1 x 2 = 2

3! = 1 x 2 x 3 = 6

4! = 1 x 2 x 3 x 4 = 24

and so on…so, n! = 1 x 2 x 3 x … x (n-2) x (n-1) x n

Logically, n! can also be expressed n x (n-1)! .

Therefore, at n=1, using n! = n x (n-1)!

1! = 1 x (0)!

which simplifies to 1 = 0!

When thinking about combinations we can derive a formula for “the number of ways of choosing k things from a collection of n things.” The formula to count out such problems is n!/k!(n-k)! For example, the number of handshakes that occur when everybody in a group of 5 people shakes hands can be computed using n = 5 (five people) and k = 2 (2 people per handshake) in this formula. (So the answer is 5!/(2! 3!) = 10).

Now suppose that there are 2 people and “everybody shakes hands with everybody else.” Obviously there is only one handshake. But what happens if we put n = 2 (2 people) and k = 2 (2 people per handshake) in the formula? We get 2! / (2! 0!). This is 2/(2 x), where x is the value of 0!. The fraction reduces to 1/x, which must equal 1 since there is only 1 handshake. The only value of 0! that makes sense here is 0! = 1.

And so we define 0! = 1.

Well, I hope that was interesting! And I feel like I have to add something more interesting into this post sooo…

I never knew you could do this! Interesting!

Well, I guess I can’t say ‘stupidity at the next level’ because, you know, they are doing maths so…

See you all next time! Keep smiling and thanks for reading!

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