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binomial expansions (1 Viewer)

Thread starter ozidolroks
Start date Jul 11, 2009

ozidolroks

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Jul 11, 2009

why is n-1 (choose) (k-1) = (n-1)(n-2)... (n-k+1)/ 1x2x3x4...x(k-1)

$\binom{n-1}{k-1}=\dfrac{(n-1)!}{(k-1)!(n-1-(k-1))!}\\\\=\dfrac{(n-1)!}{(k-1)!(n-k)!}\\\\=\dfrac{(n-1)(n-2)(n-3)....(n-k+1)(n-k)!}{(k+1)!(n-k)!}\\\\=\dfrac{(n-1)(n-2)(n-3)....(n-k+1)}{(k-1)!}\\\\=\dfrac{(n-1)(n-2)(n-3)....(n-k+1)}{1.2.3.4.....(k-2)(k-1)}$

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binomial expansions (1 Viewer)

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