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Question
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
Options
360
144
72
54
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Solution
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is 144.
Explanation:
We note that there are 3 consonants and 3 vowels E, A and O.
Since no two vowels have to be together, the possible choice for vowels are the places marked as ‘X’.
X M X C X T X, these vowels can be arranged in 4P3 ways 3 consonents can be arranged in 3 ways.
Hence, the required number of ways = 3! × 4P3 = 144.
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