Thursday, April 2, 2009

`((10),(6))` Find the binomial coefficient.

You need to evaluate the binomial coefficient, using the next formula, such that:


`((n),(k)) = (n!)/(k!(n-k)!)`


You need to replace 10 for n and 6 for k, such that:


`((10),(6)) = (10!)/(6!(10-6!) )=> ((10),(6) )=  (10!)/(6!4!)`


Notice that `10! = 6!*7*8*9*10`


` (10!)/(6!4!) = (6!*7*8*9*10)/(6!4!)  =>  ((10),(6)) =(7*8*9*10)/(1*2*3*4) = 210`


Hence, evaluating the binomial coefficient yields `((10),(6)) = 210.`

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