Question

Suppose each license plate in a certain state has two digits, followed by two letters, followed by two digits. The Q and U are not used. So, there are 24 letters and ten digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this formula?

Answer 1

5,760,000

Explanation:

You want the number of license plates that can be formed with identifiers in the form ...

<digit> <digit> <letter> <letter> <digit> <digit>

where any of the digits can be any of 0–9, and any of the letters can be any of A–Z except Q and U. Repeats are allowed.

Count

The number of possible plates is the product of the number of possibilities at each location:

10×10×24×24×10×10 = 576×10^4

5,760,000 license plates can be generated in this format.

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