Notes: `_8 C_6` Find the binomial coefficient.

Saturday, August 9, 2008

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

`nCk = (n!)/(k!(n-k)!)`

Replacing 8 for n and 6 for k yields:

`8C6 = (8!)/(6!(8-6)!) => 8C6 = (8!)/(6!*2!)`

Notice that `8! = 1*2*3*4*5*6*7*8 => 8! = 6!*7*8`

` 8C6 = (6!*7*8)/(6!*2!) => 8C6 = (7*8)/(2!) => 8C6 = (7*8)/(1*2)`

Hence, evaluating the binomial coefficient yields 8C6 = 28.

Notes