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

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: Option C

Explanation:

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!	= 10080.
	(2!)(2!)

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters =	4!	= 12.
	2!

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