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?
For the first letter, how many vowels can you possibly have?
Since the second letter can also be a vowel, but not a repetition of the first, the possibilities are one less than the number in the alphabet.
Each of the numbers can vary 0-9. How many possibilities is that?
To find the number of conbinations (either-or arrangements), you need to multiply the probabilities of the individual events.
I hope this helps, but I will let you do the calculations. Thanks for asking.
Correction. With either-or probabilities you add the probabilities of the individual events.
In your case, you want to know the probability of all of the events occurring, so you do multiply.
In this problem, the probability of any one particular arrangement is 1 over the number of possible arrangements. You still follow the process indicated above.
Sorry for my error. I hope this helps a little more. Thanks for asking.
To find the number of different license plates possible, we need to determine the number of choices for each position in the license plate.
1. The first letter must be a vowel. There are 5 vowels in the English alphabet - A, E, I, O, and U. Therefore, we have 5 choices for the first letter.
2. The second letter can be any letter except for the one already chosen for the first letter. Since repetition is not allowed, we have 25 choices for the second letter (26 letters in the alphabet minus 1 already chosen).
3. The third, fourth, and fifth positions can be any digit from 0 to 9. Therefore, we have 10 choices for each of these positions.
To calculate the total number of different license plates possible, we need to multiply the number of choices for each position:
Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter) * (number of choices for the third digit) * (number of choices for the fourth digit) * (number of choices for the fifth digit)
Number of possibilities = 5 * 25 * 10 * 10 * 10
Now, you just need to perform the calculations:
Number of possibilities = 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.