Why is the factorial of 0 equal to 1?

Question

Wouldn’t this also mean that 1!=0!, why is this true?

In: 383

Answer 1

Another way to think about factorials is to think about the number of ways you can arrange items. With zero items, there is only 1 way to arrange them.

Say you have two coins, a red one and a blue one. You can arrange the 2 coins in 2! ways. Red, then blue. Or Blue, then red.

Say you have 1 red coin. There is 1! ways to arrange them. Red coin.

Say you have 0 coins. There is 0! ways to arrange them. This gets sort of abstract, but imagine nothing. You can only arrange nothing one way, and that’s to not have anything. That’s the one way to arrange the set when there is nothing in the set. So 0! is 1.