CombinationsA 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

Combinations, cont.For example, to choose a five-card poker hand from a 52 card deck, the equation would read:

)!552(!5

!52

(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.)

!47!5

!52 = 2,598,960 variations for a poker hand

=

PermutationsA permutation is an ordered collection of distinct elements. There are two different types of objects used in permutations, distinguishable and indistinguishable.

Distinguishable

Indistinguishable

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.

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?

)!4!67(

!67

=

!63

!67= 18395520

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:

!!!

!

21 knnn

n

!3!3

!6 = 20 different arrangements