In how many different ways can the letters of the word DETAIL be arranged so that the vowels occupy only the odd positions?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36
Place the vowels first in the allowed positions, then the consonants in the rest; the two counts are multiplied.
DETAIL has 6 different letters: vowels E, A, I (3) and consonants D, T, L (3)
Odd positions among 6: 1st, 3rd, 5th, that is exactly 3 places
The 3 vowels fill these 3 places: \(3!=6\) ways
The 3 consonants fill the 3 even places: \(3!=6\) ways
Total \(=6\times6=36\)