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You are the CEO of PlatesRUs license plate manufacturing conglomerate. State regulators tell you that each...

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Basic Math

You are the CEO of PlatesRUs license plate manufacturingconglomerate. State regulators tell you that each license platemust contain 2 letters (26 possible letters, A through Z) and 3numbers (10 possible digits, 0 through 9).

a. State regulators also tell you that the numbers and letterscannot repeat (E.g., AB123 is valid, but AA123 is not). How manydifferent plates are possible? (Note: on a license plate, ordermatters. AB123 is different from BA123.)

b. Regulators have stated new rules: plates still contain 2letters and 3 numbers, but now the numbers and letters can be inany of the 5 positions. The numbers and letters still do not repeaton these new plates. (E.g., 1A23B is now valid, but 1A13B is not.)How many plates are possible now?

c. Assume now that plates are still designed as in part b,except that the no-letter-or-- number-repeat clause is not enforcedany more. What is the probability that a given plate contains thenumbers 777 in succession (i.e. right next to each other, with noletters in between)?

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