Discussion :: Permutation and Combination

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
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.
Numbers 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
Required number of words = (10080 x 12) = 120960
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