Question

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

• A. 10080
• B. 4989600
• C. 120960
• D. None of these

Answer 1

The correct option is C 120960

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
$\therefore$ Number of ways of arranging these letters $=\frac{8!}{(2!)(2!)}=10080.$
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters $=\frac{4!}{2!}=12.$
$\therefore$ Required number of words = (10080 x 12) = 120960.