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Question
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
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Solution
The word VOWELS consists of 4 consonants.
If we keep all the consonants together, we have to consider them as a single entity.
Now, we are left with the 2 vowels and all the consonants that are taken together as a single entity.
This gives us a total of 3 entities that can be arranged in 3! ways.
It is also to be considered that the 4 consonants can be arranged in 4! ways amongst themselves.
By fundamental principle of counting:
∴ Total number of arrangements = 3!\[\times\]4! = 144
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