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.
:)
