Thursday, August 26, 2010

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


Notice that `10! = 6!*7*8*9*10`


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


Hence, evaluating the binomial coefficient yields `((10),(4)) = 210.`

No comments:

Post a Comment