#### 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

$\textbf{Multiplication rule: }$If an operation costs of $k$ steps, where the first step can be performed in $n_1$ ways, the second step can be performed in $n_2$ ways, … and the $k$th step can be performed in $n_k$ ways, then the operation can be performed in $n_1n_2...n_k$ ways.

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