233k views
4 votes
A license plate consists of a letter, followed by four single-digit numbers, followed by another letter. due to possible confusion, the letters i and o are not used. repetition is not allowed. how many different license plates are possible?

User GGizmos
by
8.5k points

1 Answer

2 votes

There are 24 choices for each letter (excluding i and o) and 10 choices for each digit, making a total of 24 * 10^4 * 24 = 4840000 possible license plates.

Letters: Excluding i and o, there are 24 possible choices for each letter (A-Z excluding both i and o).

Digits: There are 10 possible choices for each of the four digits (0-9).

Total combinations: Multiplying the possible choices for each element, we get the total number of license plates: 24 choices for the first letter * 10 choices for the first digit * 10 choices for the second digit * 10 choices for the third digit * 10 choices for the fourth digit * 24 choices for the second letter. This simplifies to 24 * 10^4 * 24 = 4840000.

Therefore, due to the possible confusion with i and o, there are 4,840,000 different license plates possible with one letter at the beginning, four digits in the middle, and another letter at the end.

User Bagira
by
8.3k points