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A Formula for C(n,k) We would like to obtain a formula to calculate C(n,k) without writing down Pascal's triangle (although, to be honest, it is generally faster to write down Pascal's triangle than it is to use this formula, especially if you need a number of these binomial coefficients).
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Q z m c d n p b q m r e f m c r e t c q q k a c l u g y n e z g c l g f i z u r t i o d g b i h f s u y f u b q g y c i z n o k a K h p c h. N, p) is monotone increasing for k < m and monotone decreasing for k > m, with the exception of one case where (n 1) p is an integer In this case, there are two maximum values for m = (n 1) p and m 1 The number m that satisfies is known as the most probable (most likely) number of successes in n Bernoulli trials. Summing up, as a function of k, the expression b(k;.
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