In how many different ways can the letters of the word ‘OPTICAL’ be arranged in such a way that the vowels always come together?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 720
When some letters must stay together, they are tied into one block and the block is arranged with the other letters; then the letters inside the block are arranged among themselves.
OPTICAL has 7 different letters; the vowels are O, I and A, and the consonants P, T, C and L
The block (OIA) and the 4 consonants make 5 units: \(5!=120\) arrangements
The 3 vowels inside the block: \(3!=6\) arrangements
Total: \(120\times6=720\)