1. Combinations
A combination is an unordered collection of distinct elements.
To find a combination, the general formula is:
Where n is the number of objects from which you can choose and k is the number to be chosen

2. Combinations, cont. = = 2,598,960 variations for a poker hand
For example, to choose a five-card poker hand from a 52 card deck, the equation would read:
(This problem is a combination because the order of the arrangement of poker hand does not matter, but the cards that are in it do.) =
= 2,598,960 variations for a poker hand

3. Permutations
A permutation is an ordered collection of distinct elements. There are two different types of objects used in permutations, distinguishable and indistinguishable.
Distinguishable
Indistinguishable

4. Permutations: Distinguishable Objects
There are two ways to find the number of arrangements for permutations.
Example One: How many ways can the four chairs be arranged? 4 3 2 1
This is really the same as 4!, or 24 different arrangements.

5. Permutations: Distinguishable Objects
However, what if you only wish to select 3 of the four chairs to arrange?
In this case, the general formula permutations might come in handy:
Example Two:
How many different ways can the offices of president, vice president, secretary, and treasurer be chosen from an organization of 67 members? = =

6. Permutations: Indistinguishable Objects
Because there are more than one of each the yellow and green marbles, they become indistinguishable.
Example Three: How many different ways can the marbles be arranged?
Using the formula:
= 20 different arrangements