# Why Can't We Be Friends

Level pending

Ten people $$a_n$$, with shirts numbered from $$n = 1$$ to $$10$$ are in a meeting room. If the probability that $$a_m$$ and $$a_n$$ become friends is

$\frac{m+mn+m}{110}$

the probability that, by choosing two random people, they become friends, can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime numbers. Evaluate $$a+b$$.

×