Math Help - How to rewrite as a single combination

1. How to rewrite as a single combination

How do you rewrite 10C7 + 10C8

2. Hello, nafiro!

$\text{How do you write: }\:_{10}C_7 + _{10}\!C_8\:\text{ as a single combination?}$

We have: . $\frac{10!}{7!\,3!} + \frac{10!}{8!\,2!}$

Get a common denominator: . ${\color{red}\frac{8}{8}}\cdot\frac{10!}{7!\,3!} + \frac{10!}{8!\,2!}\cdot{\color{red}\frac{3}{3}} \;\;=\;\; \frac{8\cdot10!}{8!\,3!} + \frac{3\cdot10!}{8!\,3!}
$

And we have: . $\frac{8\cdot10! + 3\cdot10!}{8!\,3!} \;\;=\;\;\frac{11\cdot10!}{8!\,3!} \;\;=\;\;\frac{11!}{8!\,3!} \;\;=\;\; _{11}C_8$