Probability question please guide There are $5$ red and $3$ blue chips in a bowl. The red ones are numbered $1,2,3,4,5$ and the blue ones as $1,2,3$ respectively. if $2$ chips are drawn without repacement, find the probability that these chips have either the same number or the same colour.
What i think ::
For same colour, for the blue ones it will be $\binom{5}{1}*\binom{4}{1}$ and for the red ones $\binom{3}{1}*\binom{2}{1}$. So total would be, $\binom{5}{1}*\binom{4}{1}$ + $\binom{3}{1}*\binom{2}{1}$.
For the same colour, it would be, $3(\binom{5}{1}*\binom{3}{1})$.
So answer would be :: $$\frac{\binom{5}{1}*\binom{4}{1} + \binom{3}{1}*\binom{2}{1}+3(\binom{5}{1}*\binom{3}{1})}{\binom{8}{2}}$$
Is this correct? if not, then please help me.
help appreciated. This is my first post so please go easy on me if i did somthing wrong :) 

The total number of ways to choose $2$ out of $8$ chips is $\binom82=28$.
The number of ways to choose $2$ chips with the same color is $\binom52+\binom32=13$.
The number of ways to choose $2$ chips with the same number is $\min(5,3)=3$.
So the probability to choose $2$ chips with the same color or number is $\frac{3+13}{28}=\frac{4}{7}$.
