In how many different ways the letters of the word “MATHEMATICS” can be arranged so that the vowels always come together ?
A. 10080
B. 4989600
C. 120960
D. None of these
Answer : C. 120960
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! / (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.
Required number of words = (10080 x 12) = 120960.
