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?
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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.
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.
There are 1404000 different car license plates.
Answer: 1) 1757600; 2) 1404000