A license plate is to consist of two letters followed by three digits. How many different license plates are possible if the first letter must be a vowel, and repetition of letters is not permitted, but repetition of digits is permitted?
The first position can be filled in 5 ways, the second place in 25 ways (one of the 26 letters was used in the first spot), followed by each of 10 ways for the third, fourth and fifth positions.
So the number of plates = 5*25*10*10*10
=.......
What percent of the first 50 positive integers contain no odd digits?
The number of plates = 5 * 25 * 10 * 10 * 10
= 12,500.
To calculate the number of different license plates possible, we multiply the number of choices for each position.
First, we need to fill the first position with a vowel. Since there are 5 vowels (A, E, I, O, U), we have 5 choices for the first letter.
For the second position, we have to choose a letter, but it cannot be the same as the first letter. Since we used one of the 26 letters in the first position, we have 25 choices for the second letter.
For the third, fourth, and fifth positions, we can choose digits from 0 to 9, with repetition allowed. So each position has 10 choices.
Finally, we multiply the number of choices for each position to find the total number of different license plates:
Number of plates = 5 * 25 * 10 * 10 * 10
Now we can calculate it:
Number of plates = 5 * 25 * 10 * 10 * 10
= 12,500
Therefore, there are 12,500 different license plates possible if the first letter must be a vowel, repetition of letters is not permitted, but repetition of digits is permitted.