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 May 20th, 2011, 05:17 AM #1 Member   Joined: May 2011 Posts: 51 Thanks: 0 Binomial expansion as combination Hi all, I m new here In one book the author says to look at the binomial theorem as the algebraic codification of a combinatorial process. In (x+y)^n=(x+y)*(x+y)*(x+y)...n times Consider them as 'n' numbers of factors, consider 'r' as a positive integer between 0 and n. Now any r numbers of factors among those n factors will give us x^r and the rest will give us y^n-r, of the term x^r*y^n-r. Now those r factors can be chosen in nCr ways. So the co-efficient of x^r*y^n-r is nCr. I know this is right but I don't understand how... How come the co-efficient is coming as nCr? I don't understand how the co-efficient and the combination of r among n factors are linked? Cheers R  May 20th, 2011, 08:38 AM #2 Senior Member   Joined: Feb 2010 Posts: 711 Thanks: 147 Re: Binomial expansion as combination Look for example at . Expanded it equals Now look at just the term and think about where the came from. It could have come from the first parenthesis ... that is . It could have come from the second parenthesis ... that is . It could have come from the third parenthesis ... that is . It could have come from the fourth parenthesis ... that is . So the coefficient 4 is really just counting the possible arrangements of x's and y's in . That is, the coefficient is . May 20th, 2011, 04:22 PM #3 Member   Joined: May 2011 Posts: 51 Thanks: 0 Re: Binomial expansion as combination Thanks a lot, I got it Cheers R  Tags binomial, combination, expansion Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post xXxn0N00b5xXx Probability and Statistics 2 December 22nd, 2013 11:56 AM hoyy1kolko Probability and Statistics 6 December 7th, 2010 04:45 PM jsmith613 Probability and Statistics 2 December 5th, 2010 03:43 AM jsmith613 Probability and Statistics 1 November 28th, 2010 03:44 AM mikeportnoy Probability and Statistics 3 February 13th, 2009 05:37 PM

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