Notes: `_5 C_3` Find the binomial coefficient.

Monday, June 18, 2012

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

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

Replacing 5 for n and 3 for k yields:

`5C3 = (5!)/(3!(5-3)!) => 5C3 = (5!)/(3!*2!)`

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

`5C3 = (3!*4*5)/(3!*2!) => 5C3 = (4*5)/(2!) => 5C3 = (4*5)/(1*2) = 10`

Hence, evaluating the binomial coefficient yields `5C3 = 10. `

Notes