Counting

The most basic principle is multiply a*b For instance how many different ice cream combos can you make with 5 toppings and 5 flavors, 5x5=25

Permutation, Count a permutation when the order of your items matters. The easiest permutation is sets of 1, for instance, 4 runners in a race how many ways can they finish? we do n! Which is 4x3x2x1=24 different orders the racers could finish in.

Say you have 8 racers and you want to pick how many ways you can choose the top three, we use $N!/(N-R)!:8!/(8-3)!=8!/5!=8\ast 7\ast 6\ast 5\ast 4\ast 3\ast 2/5\ast 4\ast 3\ast 2=8\ast 7\ast 6=336$

Combinations Combinations are when order DOES NOT matter, for instance if ABC is the same COMBINATION as CBA. We calculate it like this: $N!/(R!\ast (n-r)!)$. It looks a lot like the permutation formula above but it the number of combinations is always smaller. (write a coin example problem here)

Principal inclusion exclusion It’s usually pretty easy to get the members of a set A and or set B, just sum up how many. But what if you want to know How many in A or B, you need to subtract the shaded region which is A and B or you will be double counting