All license plates have a letter, two characters (which are either a number or a letter) Followed by two numbers. The letter choice for the first character can only be either an E,W,P,R,A,F OR U. How many license plates can be made? What is the probability of having one with a vowel?

so a possible valid choice could be R 2S 56

All cases = 7 x 36 x 36 x 10 x 10907200
Assuming 5 vowels
number of cases without a vowel
= 4 x 31 x 31 x 10 x 10 = 3844400

prob(of having a vowel) = 1 - 384400/1090700
= appr .576

check my arithmetic

Found a typo .... forgot the = sign

should be :

All cases = 7 x 36 x 36 x 10 x 10 = 907200

To find out how many license plates can be made, we need to calculate the total number of possibilities for each character in the license plate.

For the first character, there are 7 possible choices (E, W, P, R, A, F, U).
For the second character, there are 36 possibilities (26 alphabets + 10 numbers).
For the third character, there are also 36 possibilities.
For the fourth character, there are 10 possibilities (numbers only).

To calculate the total number of license plates, we multiply the number of possibilities for each position together:

Total number of possibilities = 7 (choices for the first character) * 36 (choices for the second) * 36 (choices for the third) * 10 (choices for the fourth)

Therefore, the total number of license plates that can be made is: 7 * 36 * 36 * 10 = 90,720.

To find the probability of having one with a vowel, we need to determine how many license plates have a vowel as the first character.

Out of the 7 choices for the first character (E, W, P, R, A, F, U), 3 of them (E, A, U) are vowels.

So, the probability of having a vowel as the first character is 3 out of 7:

Probability = 3/7 = 0.4286 or 42.86%.