In how many different ways can the letters of the word ‘DIRECTOR’ be arranged so that the vowels are always… · ABC26GN5277
Subject: General Aptitude · Chapter: Permutations and Combinations
In how many different ways can the letters of the word ‘DIRECTOR’ be arranged so that the vowels are always together?
Answer
No answer key was printed for this question.
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.