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MathNet 2003 — Part 01 Question 200

Math Olympiad Vault · MathNet 2003 — Part 01

Question 200

In Italy car license plates are made up of 2 letters, followed by 3 digits and another 2 letters. In the town of Ailati things are reversed and the license plates are made up of 2 digits, followed by 3 letters and another 2 digits. Assuming that 10 digits and 22 letters are used in both countries (I, O, U, Q are not used), determine the difference between the number of all possible license plates in the two countries.
  1. 0
  2. $12 \cdot 10^{3} \cdot 22^{3}$
  3. $\left(22^{2}-10^{2}\right)^{2}-\left(22^{3}-10^{3}\right)$
  4. $12 \cdot 3 \cdot 22 \cdot 3 \cdot 10$
  5. $4^{10} \cdot 3^{10} \cdot\left(4^{12}-3^{12}\right)$.