Question

License plates in China begin with a Chinese character designating the province, followed by a letter from the set {A, ..., Z}, followed by a five-character alphanumeric string (using symbols from the set {A, ..., Z, 0, 1, ..., 9}). What is the maximum number of plates of this type for a given Chinese province?

Answer 1

The maximum number of plates are 1,572,120,576.

Explanation:

Consider the provided information.

A letter from the set {A, ..., Z}, followed by a five-character alphanumeric string (using symbols from the set {A, ..., Z, 0, 1, ..., 9}).

There are 26 alphabets, and 0 to 9 there are 10 digits.

Therefore, the set of letters for five-character alphanumeric string is:
`(26+10)^5=36^5`

Province is followed by a letter from the set of {A, ..., Z}.

Thus the maximum number of plates are:
`26* 36^5=1572120576`

Hence, the maximum number of plates are 1,572,120,576.