Question

How many words with or without meaning can be formed using the letters of the word DIFFERENTIABILITY? In how many of theses words the vowels are together?

Answer 1

vowels:  A, E, E, I, I, I, I            consonants: B,D,F,F,L,N,R,T,T,Y

1) Letters of the word: without repetition: A,E,I ,  B,D,F,L,N,R,T,Y
    Number of words that can be formed = 11 !
           the repeating letters are included once only.
    number of words in which Vowels are together = 9!  treating 3 vowels as one letter.

2) Number of words that can be formed (including repeating letters): 17 !
          number of words with vowels being together = 11 ! as all 7 vowels are treated as just one letter..