# Rolling Three Dice

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.

×