Factorials - Permutations and Combinations

Combination: probabilities selections where the order DOES NOT MATTER.

Permutation: probabilities where the order MATTERS.

Formulas:

Why is 0! = 1?

Say we take permutation formula from above, and set n = 3 and r = 3. The permutation formula with these number inputs would be:

P(3,3) = (3!)/(3-3)!

This equals 3! which means the denominator must've been 1. 

Another way to approach it:

_ _ _

We have above 3 possible slots, and we only have 3 options (A, B, C). So, our possible outcomes (when order matters) would be as follows:

A B C

B C A

C A B

B A C

C B A

A C B

*if we put the first option at the back and scoot everything over by 1 again we'll just have made a repetitive set*

B A C

Anyways, we now see we have 6 options which is indeed 3! = 1 * 2 * 3

Therefore, 0! = 1.

 :)