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.

So, 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 = \(\frac{4!}{2!}= 12\)

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