Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: 2011 · Marks: · Difficulty:
In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?
(a)810
(b)1440
(c)2880
(d)50400
(e)5760
Answer
Answer (as printed): D
Explanation
Keepting the vowels (OOAIO) together as one letter we have CRPRTN(OOAIO). This has 7 letters, out of which we have 2R, 1C, 1P, 1T and 1N. Number of ways of arranging these letters 7 7 ×6×5×4×3×2×1 = = = 2520. 2 2×1 Now, (OOAIO) has 5 letters, out of which we have 3O, 1A and 1I. Number of ways of arranging these letters 5 5 × 4 ×3 × 2 × 1 = = = 20. 3 3×2×1 ∴ Required number of ways = (2520 × 20) = 50400.
Explanation as extracted from the printed page; notation may be imperfect.