Example 14 - Find number of different 8-letter of DAUGHTER - Permutation- repeating

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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Example 14 Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that all vowels occur together Total number of letter in DAUGHTER = 8 Vowels in DAUGHTER = A, U & E Since all vowels occur together, Assume as single object. So, our word becomes Total number of arrangements = 720 × 6 = 4320 Example 14 Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that (ii) all vowels do not occur together. No of permutation in which all vowels are never together = Total number of permutation – number of permutation all vowels come together Total permutations Number of words in DAUGHTER = 8 Total no of permutation of 8 letters = 8P8 = 8!/(8 − 8)! = 8!/0! = 8!/1 = 8! = 40320 No of permutation in which all vowels are never together = Total number of permutation – number of permutation all vowels come together = 40320 – 4320 = 36000

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.