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.

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Presentation transcript:

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

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

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

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? 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: = 20 different arrangements