Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: 2012 · Marks: · Difficulty:
In how many different ways can the letters of the word CAPITAL be arranged so that the vowels always come together?
(a)120
(b)360
(c)720
(d)840
(e)None of these
Answer
Answer (as printed): B
Explanation
Keeping the vowels (AIA) together, we have CPTL (AIA). We treat (AIA) as 1 letter. Thus, we have to arrange 5 letters. These can be arranged in 5 = (5 × 4 × 3 × 2 × 1) ways = 120 ways. Now, (AIA) are 3 letters with 2A and 1I. 3 3×2×1 These can be arranged among themselves in = =3 2 2×1 ways. ∴ Required number of ways = (120 × 3) = 360.
Explanation as extracted from the printed page; notation may be imperfect.