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  • Question
  • In how many ways the letters of the word OLIVER be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right ?


  • Options
  • A. 186
  • B. 144
  • C. 136
  • D. 120

  • Correct Answer
  • 120 

    Explanation

    In given word OLIVER there are 3 vowels E, I & O. These can be arranged in only one way as dictionary order E, I & O.

     

    There are 6 letters in thegiven word.

     

    First arrange 3 vowels.

     

    This can be done in 6C3 ways and that too in only one way.(dictionary order E, I & O)

     

    Remaining 3 letters can be placed in 3 places = 3! ways

     

    Total number of possible ways of arranging letters of OLIVER = 3! x  C 3 6 ways = 6x5x4 = 120 ways.

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    Permutation and Combination problems


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    • 1. There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

    • Options
    • A. 105
    • B. 7! x 6!
    • C. 7!/5!
    • D. 420
    • Discuss
    • 2. From 5 consonants and 4 vowels, how many words can be formed using 3 consonants and 2 vowels ?

    • Options
    • A. 7600
    • B. 7200
    • C. 6400
    • D. 3600
    • Discuss
    • 3. How many arrangements of the letters of the word ?BENGALI? can be made if the vowels are to occupy only odd places.

    • Options
    • A. 720
    • B. 576
    • C. 567
    • D. 625
    • Discuss
    • 4. Find the number of subsets of the set {1,2,3,4,5,6,7,8,9,10,11} having 4 elements.

    • Options
    • A. 340
    • B. 370
    • C. 320
    • D. 330
    • Discuss
    • 5. In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels always come together?

    • Options
    • A. 720
    • B. 1440
    • C. 1800
    • D. 3600
    • Discuss
    • 6. Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

    • Options
    • A. 43929
    • B. 59049
    • C. 15120
    • D. 0
    • Discuss
    • 7. To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?

    • Options
    • A. 7920
    • B. 74841
    • C. 14874
    • D. 10213
    • Discuss
    • 8. The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is

    • Options
    • A. 7! x 7!
    • B. 7! x 6!
    • C. 6! x 6!
    • D. 7! x 5!
    • Discuss
    • 9. In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?

    • Options
    • A. 180
    • B. 220
    • C. 240
    • D. 160
    • Discuss
    • 10. How many six digit odd numbers can be formed from the digits 0, 2, 3, 5, 6, 7, 8, and 9 (repetition not allowed)?

    • Options
    • A. 8640
    • B. 720
    • C. 3620
    • D. 4512
    • Discuss


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