The Probability of Rolling the Same Number with 10 Dice That Have 19 Sides

Question

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?

Answer 1

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.

Answer 2

The probability of rolling 10 dice on the same number with 19 sides is 1*1/19*1/19*1/19*1/19*1/19*1/19*1/19*1/19*1/19, or 1/322,687,697,779 because the first die can land on any number from 1 to 19, but the other dice have to match the number on the first die.