In what ways the letters of the word puzzle can be arranged to from the different new words so that the vowels always come together?
What are the different ways in which letters of the word "PARROT" can be arranged in such a way that the vowels always come together?
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Answer (Detailed Solution Below)Option 1 : 120 ways Given: A word "PARROT" with has 5 letters from which 4 consonants and 2 vowels. Formula used: Factorial n! = n × (n - 1) × ..... × 3 × 2 × 1 Calculation: The arrangement is made in such a way that the vowels always come together. ⇒ "PRRT(AO)" Considering vowels as one letter, 5 different letters can be arranged in 5! ways. We have two "R" also = 5!/2! ⇒ 5!/2! = 60 ways The vowels "AO" can be arranged themselves in 2! ways. ⇒ 2! = ways Required number of ways = 60 × 2 = 120 ways. ∴ "PARROT" can be arranged in such a way that the vowels always come together for that we have 120 ways. Disclaimer The questions posted on the site are solely user generated, Doubtnut has no ownership or control over the nature and content of those questions. Doubtnut is not responsible for any discrepancies concerning the duplicity of content over those questions.
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