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| Combinations |
Combinations
A combination is a selection of items from a collection,where the order of selection does not matter. More formally:
A k-combination of a set S is a subset of k distinct elements of S. If the set has n elements, the number of k-combinations is equal to the binomial coefficient1
Or if you prefer using the factorial:
Combinations refer to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used and we use the following formulae:
Some examples:
Combinations are very usefull when you want to solve combinatoric problems like the following one:
Compute the probability to obtain a poker from
a standard fifty-two card deck drawing 5 cards
at the same time
In order to solve this simple problem you need to compute the number of 5 card hands possible using combinations:
Mind that is equal to 48 as per binomial coefficient definition.