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 k-element subsets (the k-combinations) of an n-element 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). Alternative notations include C(n, k), nCk or , in all of which the C stands for combinations or choices.
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Fibonacci Numbers and Binomial Coefficients The fibonacci numbers appear unexpectedly in Pascal s triangle when viewed from the right angle see Figure 3 Prove that
