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Suppose that one state’s license plates consist of 1 digit followed by 4 letters followed by 2 digits. How many such plates can the state issue?

User Balanivash
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1 Answer

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Answer:

The state can issue 456,976,000 license plates.

Explanation:

For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.

For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.

For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:


\frac{10}
\frac{26}
\frac{26}
\frac{26}
\frac{26}
\frac{10}
\frac{10}

= 10*26*26*26*26*10*10

=456,976,000.

Therefore, the state can issue 456,976,000 license plates.

User Hyunjin
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