Counting - Combinations and Permutations

If the order doesn't matter, it is a Combination.
If the order does matter, it is a Permutation. (To help you to remember, think "Permutation" as "Position".)

How many ways are there to choose r elements from a set of n elements?

Order Matters Order Does Not Matter
Repetition Is Allowed nr C(n+r-1, r) =
C(r+n-1, n-1) 		The number of ways to fill r slots from n catgories with repetition allowed.
Repetition Is Not Allowed P(n,r) C(n,r)

P(n,r) = n! / (n-r)!

C(n,r) = n! / r!(n-r)!

How many ways can I select 12 cans of soda from a cooler containing large quantities of Coke, Pepsi, Diet Coke, Root Beer and Sprite?  ___________

Answer: C(12 + 4 - 1, 4 - 1)