Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: · Marks: · Difficulty:
In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?
(a)120
(b)48
(c)72
(d)168
(e)None of these
Answer
Answer (as printed): C
Explanation
Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters. These letters can be arranged in 4 = 24 ways. The letters EA may be arranged amongst themselves in 2 ways. Number of arrangements having vowels together = (24 × 2) = 48 ways. Total arrangements of all letters = 5 = (5 × 4 × 3 × 2 × 1) = 120. Number of arrangements not having vowels together = (120 – 48) = 72.
Explanation as extracted from the printed page; notation may be imperfect.