1. | In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? |
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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.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Required number of words = (10080 x 12) = 120960. |

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