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Combination - Monomath Math Dictionary
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C

Combination

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๐Ÿ“– Definition

A combination is a selection of items from a larger set where order does not matter.

๐Ÿ“ Detailed Explanation

The number of ways to choose k items from n items is denoted C(n,k) or โฟCโ‚–, read as "n choose k." The formula is C(n,k) = n! / (k!(n-k)!). Combinations differ from permutations in that order does not matter. For example, choosing 3 students from a class of 10 is a combination. Combinations are used in probability, lottery odds, poker hands, and binomial expansions.

๐Ÿ“ Formula

C(n,k) = n! / (k!(n-k)!)

๐Ÿ“œ History & Origins

Combinations were studied in ancient India and China for poetic meter and mathematical games. The binomial coefficients were arranged in Pascal's Triangle by Blaise Pascal in 1654, though the triangle was known in China and Persia centuries earlier. The modern notation โฟCแตฃ was introduced by Andreas von Ettingshausen in 1826.

๐Ÿ”— Related Terms

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