[Math] Number of license plates formed by four digits and one letter, qualified.

combinatoricspermutations

I need some help with this question:

If a license plate for a vehicle consist of five characters: $4$ digits (the first of
which cannot be $0$), followed by one letter of the alphabet (which
cannot be $I$ or $O$), how many different license plates are possible?

Best Answer

We have a license plate format:

  • first digit from $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}:\;$ 9 choices
  • second, third, fourth digit from $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}:\;$ 10 choices, for each place.
  • fifth position: one of 24 letters (26 letters of alphabet, minus the two distinct letters not allowed) gives 24 choices.

Using the rule of the product, that gives us:

$$9 \times 10 \times 10 \times 10 \times 24 = 9 \times 10^3 \times 24 = 216,000\;\text{license plates available}$$

Related Question