Suppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1–3 are to choose the uppercase letters to put in positions 1–3 and the remaining steps are to choose the digits to put in the remaining positions. There are  ways to perform steps 1–3, and there are  ways to perform the remaining steps. Thus, the number of license plates is  . (b) How many license plates could begin with A and end in 0? In this case, the number of ways to place the A in Step 1 is  and the number of ways to place the 0 in the final step is  . Thus, the answer is  . (c) How many license plates could begin with UVA? In this case, the number of ways to perform steps 1–3 is  . Thus, the answer is  . (d) How many license plates are possible in which all the letters and digits are distinct?   (e) How many license plates could begin with AB and have all letters and digits distinct?

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