How is 0! 1?

If you have no cards there are no possibilites

right?

K ig

The Factorial Function (denoted by “n!”) represents the multiplication of every integer from that number down to 1.

For example, 3! = 3 × 2 × 1 = 6.

In your case of 0!, it equals 1 for two reasons.

The first reason is that the factorial function is also the number of ways we can arrange a set with that many elements in them.

Imagine a set with 3 elements in them. {A, B, C}. We can arrange them: {A, B, C}, {B, A, C}, {C, A, B}, {B, C, A}, {A, C, B}, and {C, B, A}. There are six ways to arrange those 3 elements, so 3! = 6.

Another way we can look at it, is by trying to work backwards. (n-1)! = n! / n, so we can work backwards from, say, 3!, to find 0!. 3! = 6, and 6 ÷ 3 = 2, meaning that 2! = 2. 2 ÷ 2 = 1, so 1! = 1. And 1 ÷ 1 = 1, so 0! must equal 1.

You can see this website for more information!