# How do use the binomial theorem to calculate 6C4?

Apr 17, 2017

$15$

#### Explanation:

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

"^6 C _4 = (6!)/((6-4)! * 4!) = (6!)/(2! * 4!)

$= \frac{6 \cdot 5 \cdot \cancel{4} \cdot \cancel{3} \cdot \cancel{2} \cdot \cancel{1}}{\left(2 \cdot 1\right) \cdot \left(\cancel{4} \cdot \cancel{3} \cdot \cancel{2} \cdot 1\right) \cdot}$

$= \frac{6 \cdot 5}{2 \cdot 1} = 15$

Dec 9, 2017

This question requires a basic understanding of how to manipulate factorials.

""^6C_4=15