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Question
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
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Solution
Number of vowels = 2
Number of consonants = 5
Considering the two vowels as a single entity, we are now to arrange 6 entities taken all at a time.
Total number of ways = 6!
Also, the two vowels can be mutually arranged amongst themselves in 2! ways.
By fundamental principle of counting:
Total number of words that can be formed = 6!\[\times\]2! = 1440
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