Question

How many different plates can be made with 2 vowels and a digit?

Answer 1

Answer:  750

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Explanation:

If repeats are allowed, then we have 5 vowels (a,e,i,o,u) for the first vowel slot, and 5 choices for the second vowel slot. We also have 10 choices for the numeric digit (0 through 9).

There are 5*5*10 = 250 ways to make a selection of the form LLN where L stands for "letter" (specifically a vowel) and N stands for "number". An example plate could be AE2.

There are also 250 ways to make a selection of the form LNL and 250 ways to select something of the form NLL.

That means there are 3*250 = 750 ways to make a license plate with two vowels and a digit where repeats are allowed.