# How do you find the binomial coefficient of 8C6?

Mar 11, 2017

""^8C_6 = 28

#### Explanation:

We want to calculate:

( (8), (6) ) = ""^8C_6

We can either use a calculator, if you have that functionality. It is often labelled ""^nC_r

""^8C_6 = 28

On advanced TI calculators (eg TI-nspire), you use the $n c r$ function:

$n c r \left(8 , 6\right) = 28$

Otherwise we calculate using the definition:

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

Which gives us:

""^8C_6 = (8!)/(6!(8-6)!)
 " "= (8!)/(6!2!)
$\text{ } = \frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{\left(1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6\right) \left(1 \cdot 2\right)}$
$\text{ } = \frac{7 \cdot 8}{2}$
$\text{ } = 7 \cdot 4$
$\text{ } = 28$