41 lines
1.9 KiB
Markdown
41 lines
1.9 KiB
Markdown
---
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title: Combinations
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---
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## Combinations
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A combination is a selection of items from a collection,where the order of selection does not matter. More formally:
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>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 coefficient](https://guide.freecodecamp.org/mathematics/counting/factorials-and-binomial-coefficients/)<sup>1</sup>
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Or if you prefer using the [factorial](https://guide.freecodecamp.org/mathematics/counting/factorials-and-binomial-coefficients/):
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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:
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## Some examples:
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Combinations are very usefull when you want to solve combinatoric problems like the following one:
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```
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Compute the probability to obtain a poker from
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a standard fifty-two card deck drawing 5 cards
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at the same time
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```
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In order to solve this simple problem you need to compute the number of 5 card hands possible using combinations:
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Mind that  is equal to 48 as per binomial coefficient definition.
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### Sources
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1 [Wikipedia Combination entry](https://en.wikipedia.org/wiki/Combination)
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