Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: 2002 · Marks: · Difficulty:
In how many different ways can the letters of the word ‘DETAIL’ be arranged so that the vowels occupy only the odd positions?
Answer
Answer (as printed):
Explanation
There are 6 letters in the given word, out of which there are 3 consonants and 3 vowels. Let us mark these positions as (1) (2) (3) (4) (5) (6). Now, 3 vowels can be placed at any of 3 places, marked 1, 3, 5. Number of these arrangements = 3P3 = 3 = 6. Also, 3 consonants can be placed at the remaining 3 places. Number of these arrangements = 3P3 = 3 = 6. Total number of ways = (6 × 6) = 36.
Explanation as extracted from the printed page; notation may be imperfect.