How many different license plates are possible if each contains 3 letters (out of the alphabet's 26 letters) followed by 2 digits (from 0 to 9) ? How many of these license plates contain no repeated letters and no repeated digits?

The number of ways the license plates contain no repeated letters and no repeated digits = 1,404,000

Step-by-step explanation:

The total number of alphabet's = 26

The total number of digits = 10 (0 - 9)

The number plate contains 3 letters followed by 2 digits.

The number of ways the license plates contain no repeated letters and no repeated digits.

The number of ways first letter can be filled in 26 ways.

The number of ways second letter can be filled in 25 ways.

The number of ways third letter can be filled in 24 ways.

The number of ways the first digit can be in 10 ways

The number of ways the second digit can be in 9 ways.

The number of ways the license plates contain no repeated letters and no repeated digits = 26 * 25 * 24 * 1 0 * 9

The number of ways the license plates contain no repeated letters and no repeated digits = 1,404,000