A choose b

Here is the formula for a choose b: $\binom{a}{b}=\frac{a!}{b!(a-b)!}$ . This is assuming that of course $a \ge b$ .

Why is it important?

a choose b counts the number of ways you can pick b things from a set of a things. For example $\binom{8}{2}=\frac{8!}{2!(8-2)!}=\frac{8(7)}{2}=\frac{42}{2}=21$ . More at https://artofproblemsolving.com/videos/counting/chapter4/64.

Here is a list of n choose 2's

$\binom{2}{2}=1$

$\binom{3}{2}=3$

$\binom{4}{2}=6$

$\binom{5}{2}=10$

These are triangle numbers! Here is my proof: