Question

How do you evaluate `""^12C_6`?

Answer 1

`""^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...