Question

Suppose that in a certain state, all automobile license plates have four letters followed by three digits. a. How many different license plates are possible? b. How many license plates could begin with A and end in 0? c. How many license plates could begin with TGIF? 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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DEFINITIONS

Multiplication rule: \textbf{Multiplication rule: }If an operation costs of kk steps, where the first step can be performed in n1n_1 ways, the second step can be performed in n2n_2 ways, … and the kkth step can be performed in nkn_k ways, then the operation can be performed in n1n2...nkn_1n_2...n_k ways.

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