# How do you evaluate ""^12C_6?

Jan 27, 2017

""^12C_6 = 924

#### Explanation:

The general formula for combinations is:

""^nC_r = (n!)/(r!(n-r)!)

So in our example:

""^12C_6 = (12!)/(6!6!)

color(white)(""^12C_6) = (12xx11xx10xx9xx8xx7)/(6xx5xx4xx3xx2xx1)

color(white)(""^12C_6) = (2^6xx3^3xx5xx7xx11)/(2^4xx3^2xx5)

color(white)(""^12C_6) = 2^2xx3xx7xx11

color(white)(""^12C_6) = 924

Or you can write out Pascal's triangle to the $13$th row and pick the middle term in that row...