# Thread: How many licence plates

1. ## How many licence plates

hello,
a question if you have a licence plate with 3 letters i.e QWE ,ASE, SDF etc how many licence plates will you have if the last letter ended with a vowel i.e WEI, DSA,AWE
repetions are not permitted.

2. I see that you have only fifteen postings.
But by now you should understand that this is not a homework service
So you need to either post some of your own work on a problem or you need to explain what you do not understand about the question.

3. I am aware that this is not a homework service but if you would have read my 15 post you could see that for the vast majority I have clearly made some effort and always do, I would not be asking otherwise, my question is more of a confirmation of what I read in a book and incidentally I am not some insulent student trying to hand in some last minute assignment but do a little mathematics out of love for the subject. So,
In the book it claimed the answer was 5.25.24 is this correct ? from the little I understand about combinatorics there should be atleast 4 cases :

case 1: no vowels in which case you would get 26.25.5
case 2 : 2 vowels in which case you would get 26.25.3
case 3 : choose 1 vowels first then 1 non vowel second in which case you would get 26.25.4
case 4 : choose 1 non vowels first then 1 vowel second in which case you would get 26.25.4
Thus, summing you cases you get,

26.25.5 + 26.25.3 + 26.25.4 + 26.25.4 = 26.25 (5 + 3 + 4 + 4) = 26.25.16 = 10,400 choices

Thank you.

4. The answer given is correct.
Think of it this way. Begin at the right hand end.
There are five choices of a vowel; there are 25 choices for the next position and 24 choices for the third position.
$\displaystyle 5\cdot 25\cdot 24$

5. Thank you !