Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: · Marks: · Difficulty:
In how many different ways can the letters of the word ‘DAUGHTER’ be arranged so that the vowels always come together?
Answer
Answer (as printed):
Explanation
The given word contains 8 different letters. When the vowels AUE are taken together, we may treat them as 1 letter. Then, the letters to be arranged are DGHTR (AUE) The vowels can be arranged in 6P6 = 6 = 720 ways. The vowels AUE may be arranged in 3 = 6 ways. Required number of ways = (720 × 6) = 4320 ways. PERMUTATIONS AND COMBINATIONS 843
Explanation as extracted from the printed page; notation may be imperfect.