How many different car license plates can be constructed if the licenses contain three letters followed by two digits if repetitions are allowed? If repetitions are not allowed?

There are 26 letters (A-Z) and 10 digits (0-9)

1) repetitions are allowed

We can choose each of the first three positions in 26 ways.

Fourth and fifth positions can be chosen in 10 ways.

$26\cdot 26\cdot 26\cdot 10\cdot 10= 1757600$

There are 1757600 different car license plates.

2) repetitions are not allowed

We can choose first position in 26 ways, second position in 25 ways, third position in 24 ways, fourth position in 10 ways, and fifth position in 9 ways.

$26\cdot 25\cdot 24\cdot 10\cdot 9=1404000$

There are 1404000 different car license plates.

Answer: 1) 1757600; 2) 1404000