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

Correct Answer: Option C

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.

Number of ways of arranging these letters = 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

= 4!/2!= 12.

So, Required number of words = (10080 x 12) = 120960.