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?
Answer (Detailed Solution Below)
Option 1 : 120 ways
A word "PARROT" with has 5 letters from which 4 consonants and 2 vowels.
Factorial n! = n × (n - 1) × ..... × 3 × 2 × 1
The arrangement is made in such a way that the vowels always come together.
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.
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