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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?
How many different ways can the letters of the word 'mathematics' be arranged so that the vowels always come together?
This is a permutation problem where we can treat the vowels together as a single entity. That entity consists of the letters A, E, I. Since there are six vowels in total, we have to find the permutation of 7 entities, where 4 entities are consonants (M, T, H, C, S), and the other 3 are the vowels entity. The answer would be 4! * 3! = 144.