Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: · Marks: · Difficulty:
In how many different ways can the letters of the word ‘DIRECTOR’ be arranged so that the vowels are always together?
Answer
Answer (as printed):
Explanation
In the given word, we treat the vowels IEO as 1 letter. Thus, we have DRCTR (IEO). This group has 6 letters in which R occurs 2 times and other are all different. 6 (6 × 5 × 4 × 3 × 2 × 1) Number of ways of arranging these letters = = = 360. 2 2 Now, 3 vowels can be arranged among themselves in 3 = 6 ways. ∴ Required number of ways = (360 × 6) = 2160.
Explanation as extracted from the printed page; notation may be imperfect.