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Licence plates consist of either 3 letters and 3 numbers or 4 letters and 3 numbers. How many different licence plates can be issued?

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Answer to a math question Licence plates consist of either 3 letters and 3 numbers or 4 letters and 3 numbers. How many different licence plates can be issued?

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Jett
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43 Answers
To find the number of different license plates that can be issued, we need to consider each type separately and then add them together.

For the first type, with 3 letters and 3 numbers, we have:
- There are 26 letters in the alphabet, so we have 26 choices for each of the 3 letter positions.
- There are 10 digits (0-9) for the number positions.
- Therefore, the total number of different license plates for this type is 26^3 \times 10^3 .

For the second type, with 4 letters and 3 numbers, we have:
- 26 choices for each of the 4 letter positions.
- 10 choices for each of the 3 number positions.
- Therefore, the total number of different license plates for this type is 26^4 \times 10^3 .

To find the total number of all possible license plates, we add the results from the two types:
26^3 \times 10^3 + 26^4 \times 10^3 = 26^3 \times 10^3 (1 + 26) = 26^3 \times 10^3 \times 27

Answer: The total number of different license plates that can be issued is 474552000 .

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