In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come… · ABC26GN5321
Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: Bank P.O. 2011
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.