+0

# 0!=1???

0
225
2

Why does

0! = 1

?

Guest Apr 10, 2015

#2
+91435
+13

0!=1

I could just say that it is define that way which is certainly true.

or I could say that 0! is the number of ways that 0 items can be odered - that would be just one way.

Now

5C1 is the number of ways that 1 item can be  chosen from 5 it equals      $$^5C_1=\frac{5!}{1!(5-1)!}=\frac{5!}{1*4!}=5\\\\$$

5C0 is the number of ways that 0 item can be  chosen from 5 it equals  [the answer has to be 1 there is only one way of chosing nothing]

$$\\^5C_0=\frac{5!}{0!(5-0)!}=\frac{5!}{0!*5!}=\frac{1}{0!}\\\\  the only way this can work is if 0!=1\\\\ so\\\\ 0!=1$$

Melody  Apr 10, 2015
Sort:

#1
+80935
+5

Here's an  informal "proof"....

3! =  4! / 4

2! =  3! / 3

1!  = 2!/ 2

So, by extension

0!   = 1! / 1    = 1

CPhill  Apr 10, 2015
#2
+91435
+13

0!=1

I could just say that it is define that way which is certainly true.

or I could say that 0! is the number of ways that 0 items can be odered - that would be just one way.

Now

5C1 is the number of ways that 1 item can be  chosen from 5 it equals      $$^5C_1=\frac{5!}{1!(5-1)!}=\frac{5!}{1*4!}=5\\\\$$

5C0 is the number of ways that 0 item can be  chosen from 5 it equals  [the answer has to be 1 there is only one way of chosing nothing]

$$\\^5C_0=\frac{5!}{0!(5-0)!}=\frac{5!}{0!*5!}=\frac{1}{0!}\\\\  the only way this can work is if 0!=1\\\\ so\\\\ 0!=1$$

Melody  Apr 10, 2015

### 3 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details