# How do you evaluate 6C3?

Jul 21, 2016

""^6C_3=20

#### Explanation:

""^nC_r is selection of $r$ possible combinations of objects from a set of $n$ objects.

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

Hence ""^6C_3=(6!)/(3!xx(6-3)!)

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

= $\frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 5 \times 4 = 20$