Repeated digit on a plate

A license plate is 22 letters (AAZZ) followed by 33 digits (0099). How many plates have at least one repeated digit among the three digits (the letters are unrestricted)?

Show hints (2)+
  1. Count the complement: plates whose three digits are all distinct.
  2. 262103262(1098)26^2\cdot 10^3 - 26^2\cdot(10\cdot 9\cdot 8).

Answer

Reveal answer →

189280

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: Probability & Market-Making, EV & Betting Games

Related questions