There are three fair six-sided dice with sides $0,1,e,\pi,i,\sqrt2$. If these dice are rolled, the probability that the product of all the numbers is real can be expressed as $\frac ab$ where $a$ and $b$ are positive, co-prime integers. What is $a+b$?
When I tried I got the total possibilities to be 216 and the rest I got wrong. Can you help me find the answer to the problem? (I think it is $\frac{99}{216}$).