RAINBOW has 4 Consonants and 3 vowels.
Out of 3Vowels 2 vowel are selected and arranged in 3P2 ways
and the rest letters are arranged in 5! ways(1vowel and 2 consonants)
The Required arrangement is: 3P2*5!=720
But the Ans is 2880
Out of 7 possible ways subract the one having either all vowel together or no vowel are together.
7!-(5!*3!+4!*5P3!)=2880 // i got the answer through this approach
What i have done wrong in ist approach and why the approach was wrong?