In how many different ways can the letters of the word ‘DETAIL’ be arranged so that the vowels occupy only… · ABC26GN5279
Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: Bank P.O. 2002
In how many different ways can the letters of the word ‘DETAIL’ be arranged so that the vowels occupy only the odd positions?
Answer
No answer key was printed for this question.
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.