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

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 .