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 | n^{r} | 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)