Question:
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
[A].10080
4989600
120960
None of these
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
[A].
[B].
[C].
[D].
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.