The Probability of Rolling the Same Number with 10 Dice That Have 19 Sides I like dice and I want to know what the probability is for rolling the same number with 10 dice that have 19 sides.  Also, do these dice exist or not?

You are rolling $10$ dice each with $19$ sides. 
The first die can land on anything, but then all of the rest have to land on that same number. 
The chance that each die lands on this number is $\frac{1}{19}$ since they have 19 sides. And since our rolls are independent, this means we have a probability of
$$\frac{1}{19^{9}}$$
to roll the same number on every die. 
