In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels… · ABC26GN5315
Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: Bank P.O. 2010
In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels always come together?
(a)30
(b)48
(c)144
(d)576
(e)None of these
Answer
Answer (as printed): D
Explanation
The given word contains 7 different letters. Keeping the vowels (AUIO) together, we take them as 1 letter. Then, we have to arrange the letters CTN(AUIO). Now, 4 letters can be arranged in 4 = 24 ways. The vowels (AUIO) can be arranged among themselves in 4 = 24 ways. ∴ Required number of ways = (24 × 24) = 576.
Explanation as extracted from the printed page; notation may be imperfect.