posted by Carlos on .
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.