In how many different ways, can the letters of words OPTICAL be arranged so that the vowels are never together?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4320
OPTICAL has 7 distinct letters, of which O, I and A are vowels, so the total number of arrangements is 7! = 5040.
Treating the three vowels as one block gives 5 units, which can be arranged in 5! ways with the vowels rearranged among themselves in 3! ways: 120 × 6 = 720 arrangements with the vowels together. Subtracting, 5040 − 720 = 4320.