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.
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