I saw the license plate 888-UUU the other day and wondered what the probability was a plate with 3 of the same number and letter. Our states license plate format is 3 numbers and 3 alphabetic characters.
2026-04-13 05:51:42.1776059502
What is the probability of getting license plate 888-UUU
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1
Of course there are assumptions in this game (as always with applications of probability theory to reality). We assume that all for the first three digits all of the numbers $\{0,\dots, 9\}$ are equally likely (and independent), and the same for the three characters chosen from $\{A,\dots, Z\}$.
We want to know the probability that we obtain a set of three identical letters when uniformly and randomly chose from a set of $n$ elements. The total number of results is given by $n^3$. Obtaining three identical elements, means that the first element can be anything (n possibilities), while the rest is fixed. Thus, we have $$P(\text{three same}) = \frac{n}{n^3} = \frac{1}{n^2}\;.$$
In you case, we have $n=10$ for the numbers and $n=26$ for the characters, thus the result reads $$P = \frac{1}{10^2}\cdot \frac{1}{26^2} \;.$$