write all permutation of examination if the vowels are never together
Answers
Answer:
There are 5 letters in the word OMEGA
(i) When O and A occupying end places M,E,G,(OA)
The first 3 letters can be arranged in 3! ways and the letters O,A can be arranged in 2! ways.
∴ Total number of such ways = 6×2=12 ways
(ii) When E is fixed in the middle, the remaining 4 words can be arranged in 4! ways.
∴ Total number of such words = 4!= 24 ways
(iii) Three vowels (O,E,A) can be arranged in the odd places in 3! ways and the two consonants can be arranged in 2! ways.
∴ Total number of such words = 3!×2!= 12 ways
(iv) Total number of words = 5! = 120
Combine the vowels into one bracket as (OEA) and treating them as one letter we have three letters (OEA),M,G and these can be arranged in 3! ways and three vowels can be arranged in 3! ways.
∴ Number of ways when the vowels come together = 3!×3! = 36 ways
Hence, the number of ways when vowels being never together = 120−36=84 ways
The required answer =
6
84−12−24−12
=6