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  • Question
  • In how many ways can the letters of the word 'Director' be arranged so that the three vowels are never together?


  • Options
  • A. 1800
  • B. 18000
  • C. 16000
  • D. 1600

  • Correct Answer
  • 18000 

    Explanation

    Total number of letters = 8
    Number of vowels = 3 and r occurs twice.
    Total number of arrangements when there is no restriction = 8!/2!

    When three vowels are together, regarding them as one letter, we have only 5 + 1 = 6 letters
    These six letters can be arranged in 6!/2! ways, since r occurs twice.
    But the three vowels can be arranged among themselves in 3! ways.
    Hence number of arrangement when the three vowels are together = 6! /(2 !x 3!)

    ? Required number = 8!/2! - {6! / (2! x 3!)} = 18,000


  • Permutation and Combination problems


    Search Results


    • 1. 
      Vowels being never together.

    • Options
    • A. 36 ways
    • B. 84 ways
    • C. 120 ways
    • D. 10 ways
    • Discuss
    • 2. 
      Vowels occupying odd places .

    • Options
    • A. 12 ways
    • B. 16 ways
    • C. 6 ways
    • D. 20 ways
    • Discuss
    • 3. 
      E being always in the middle.

    • Options
    • A. 18 ways
    • B. 24 ways
    • C. 48 ways
    • D. 20 ways
    • Discuss
    • 4. 
      O and A occupying end places.

    • Options
    • A. 12
    • B. 14
    • C. 20
    • D. 18
    • Discuss
    • 5. 
      In how many ways, can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

    • Options
    • A. 15!/(8!)
    • B. 7!/88!
    • C. 15C8 x 6! x 7!
    • D. 15C8 x 8!
    • Discuss
    • 6. 
      A mixed doubles tennis game is to be played between two teams ( each team consists of one male and one female). There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

    • Options
    • A. 12
    • B. 48
    • C. 36
    • D. 42
    • Discuss
    • 7. 
      There is a 7-digit telephone number with all different digits. If the digit at extreme right and extreme left are 5 and 6 respectively, find how many such telephone number are possible?

    • Options
    • A. 120
    • B. 100000
    • C. 6720
    • D. 30240
    • Discuss
    • 8. 
      In how many ways, can 24 persons be seated around a circular table if there are is 13 seats?

    • Options
    • A. 24! / [13 x 11! ]
    • B. 22! / [14 x 12!]
    • C. 23! / [13 x 11!]
    • D. 24! / [12 x 12!]
    • Discuss
    • 9. 
      There are 14 points in a plane, out of which 4 are collinear. Find the number of triangles made by these points .

    • Options
    • A. 364
    • B. 360
    • C. 368
    • D. 365
    • Discuss
    • 10. 
      A question paper consists of two sections having respectively 3 and 5 questions. The following note is given on the paper. "It is not necessary to attempt all the question". One question from each section is compulsory. In how many ways, a candidate can select the question?

    • Options
    • A. 38
    • B. 217
    • C. 256
    • D. 320
    • Discuss


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