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In mathematics, the binomial coefficient is the coefficient of the x^{ k} term in the polynomial expansion of the binomial power (1 + x)^{ n}.
In combinatorics, is interpreted as the number of kelement subsets (the kcombinations) of an nelement set, that is the number of ways that k things can be "chosen" from a set of n things. Hence, is often read as "n choose k" and is called the choose function of n and k.
The notation was introduced by Andreas von Ettingshausen in 1826,^{[1]} although the numbers were already known centuries before that (see Pascal's triangle). The earliest known detailed discussion of binomial coefficients is in a tenthcentury commentary, due to Halayudha, on an ancient Hindu classic, Pingala's chandaḥśāstra. In about 1150, the Hindu mathematician Bhaskaracharya gave a very clear exposition of binomial coefficients in his book Lilavati.^{[2]}
Alternative notations include C(n, k), _{n}C_{k}, ^{n}C_{k}, ,^{[3]} in all of which the C stands for combinations or choices.
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