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

Correct Answer: 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! x 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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