The English alphabet has 26 letters, 5 of these are vowels.
How many permutations of English letters are there in which all vowels are in consecutive places?
There are C(26,5) + C(26,26-5) = C(26,5) + C(26,21) = 2·C(26,5) = 2·65780 = 131560 permutations.
Is my answer correct? If not, please explain how one should address this problem. Thanks.