Question
In how many different ways can the letters of the word `MATHEMATICS` be arranged so hat the vowels always come together ?
Answer: Option C
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In the word `MAHEMATICS` 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.
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