Rolling Three Dice

Probability Level 3

Three standard dice, one with 4 sides, one with 6 sides, and one with 10 sides are rolled. The probability that all three dice show the same number can be expressed as $\frac{a}{b}$ where $a$ and $b$ are positive coprime integers. What is the value of $a + b?$

Details and assumptions

A standard $i$ -sided die has sides numbered $1, 2, \ldots, i$ and each rolls with equal probability.