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  • Question
  • In how many ways the letters of the word 'CIRCUMSTANCES' can be arranged such that all vowels came at odd places and N always comes at end?


  • Options
  • A. 1,51,200 ways.
  • B. 5,04,020 ways
  • C. 72,000 ways
  • D. None of the above

  • Correct Answer
  • 1,51,200 ways. 

    Explanation

    In circumcstances word there are 3C's, 2S's, I, U,R, T, A, N, E

    Total = 13 letters

    But last letter must be N

    Hence, available places = 12

    In that odd places = 1, 3, 5, 7, 9, 11

    Owvels = 4

    This can be done in 6P4 ways 

    Remaining 7 letters can be arranged in 7!/3! x 2! ways

     

    Hence, total number of ways = 6P4 x 7!/3! x 2! = 360 x 5040/12 = 1,51,200 ways.

  • Tags: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO

    Permutation and Combination problems


    Search Results


    • 1. In how many ways can the letters of the word 'LEADER' be arranged ?

    • Options
    • A. 360
    • B. 420
    • C. 576
    • D. 220
    • Discuss
    • 2. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed ?

    • Options
    • A. 5040
    • B. 2525
    • C. 2052
    • D. 4521
    • Discuss
    • 3. If the letters of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word VERMA is :

    • Options
    • A. 108
    • B. 117
    • C. 810
    • D. 180
    • Discuss
    • 4. There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?

    • Options
    • A. 70
    • B. 40
    • C. 72
    • D. 80
    • Discuss
    • 5. When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?

    • Options
    • A. 15
    • B. 42
    • C. 16
    • D. 40
    • Discuss
    • 6. A box contains 5 green, 4 yellow and 3 white marbles. Threemarbles are drawn at random. What is the probability thatthey are not of the same colour ?

    • Options
    • A. 40/44
    • B. 44/41
    • C. 41/44
    • D. 40/39
    • Discuss
    • 7. In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?

    • Options
    • A. 2800
    • B. 2880
    • C. 2600
    • D. 3980
    • Discuss
    • 8. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

    • Options
    • A. 564
    • B. 735
    • C. 756
    • D. 657
    • Discuss
    • 9. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

    • Options
    • A. 48
    • B. 64
    • C. 63
    • D. 45
    • Discuss
    • 10. A standard deck of playing cards has 13 spades. How many ways can these 13 spades be arranged?

    • Options
    • A. 13!
    • B. 13^2
    • C. 13^13
    • D. 2!
    • Discuss


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