Question

A license plate begins with three letters and three numbers. If the possible letters are all vowels only, and the number choices for each digit will only be odd numbers, how many different license plate can be made if no letter and number is used more than once?

Answer 1

For the creation of unique license plates with the given constraints, you can have 1440 different combinations when selecting from four unique vowels and five unique odd numbers each without repetition.

Step-by-step explanation:

The question involves calculating the number of different license plates that can be created with specific constraints on letters and numbers. For a license plate that begins with three letters and ends with three numbers:

1. Vowels: There are 5 standard vowels (A, E, I, O, U), but since we cannot use any letter more than once and only four are always vowels, our choices are limited to these four. Hence, for the first letter, we have 4 options, for the second letter 3 options (since one has been used), and for the third letter 2 options remaining.
2. Odd numbers: We have 5 odd digits (1, 3, 5, 7, 9) to choose from. Following a similar logic as with the letters, for the first number we have 5 options, for the second number 4 options remaining, and for the third number 3 options.

Multiplying the choices together, we arrive at the total number of unique license plates: 4 x 3 x 2 x 5 x 4 x 3 = 1440 different license plates.