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Home Aptitude Permutation and Combination Comments

  • Question
  • The total number of words, which can be formed out of the letters a, b, c, d, e, f taken 3 together, such that each word contains at least one vowel is?


  • Options
  • A. 72
  • B. 48
  • C. 96
  • D. None of these

  • Correct Answer
  • 96 

    Explanation

    The required number of words is : (2C1 x 4C2 + 2C2 x 2C1) 3! = 96


  • Permutation and Combination problems


    Search Results


    • 1. 
      4 boys and 2 girls are to be seated in a row in such a way that two girls are always together. In how many different ways can they be seated?

    • Options
    • A. 120
    • B. 720
    • C. 148
    • D. 240
    • Discuss
    • 2. 
      A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separated?

    • Options
    • A. 120
    • B. 180
    • C. 160
    • D. 140
    • Discuss
    • 3. 
      There are 20 books of which 4 are single volumes and the other are books of 8, 5 and 3 volumes respectively. In how many ways can all these books be arranged on a self so that volumes of the same book are not separated?

    • Options
    • A. 7! 8! 5! 3!
    • B. 7! 8! 4! 3!
    • C. 7! 6! 5! 3!
    • D. None of these
    • Discuss
    • 4. 
      How many different letter arrangements can be made from the letter of the word RECOVER?

    • Options
    • A. 1210
    • B. 5040
    • C. 1260
    • D. 1200
    • Discuss
    • 5. 
      Letters of the word DIRECTOR are arranged in such a way that all the vowels come together. Find out the total no. of ways for making such arrangement.?

    • Options
    • A. 4320
    • B. 2720
    • C. 2160
    • D. 1120
    • Discuss
    • 6. 
      A man has 5 friends and his wife has 4 friends. They want to invite either of their friends, one or more to a party. In how many ways can they do so?

    • Options
    • A. 9
    • B. 18
    • C. 31
    • D. 46
    • Discuss
    • 7. 
      If there are 10 positive real numbers n 1 < n 2, n 3 .... < n 10 How many triplets of these numbers (n 1, n 2, n 3) (n 2, n 3, n 4), ... can be generated such that in each triplet the first number is always less than the second number and the second number is always less the third number?

    • Options
    • A. 45
    • B. 90
    • C. 120
    • D. 180
    • Discuss
    • 8. 
      How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

    • Options
    • A. 990
    • B. 2730
    • C. 12870
    • D. 1560000
    • Discuss
    • 9. 
      A question paper had 10 questions. Each question could only be answered as True (T) or false (F). Each candidate answered all the questions. Yet, no two candidate wrote the answers in an identical sequence. How many different sequences of answers are possible?

    • Options
    • A. 20
    • B. 40
    • C. 512
    • D. 1024
    • Discuss
    • 10. 
      Groups, each containing 3 boys are to be formed out of 5 boys, A, B , C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?

    • Options
    • A. 5
    • B. 6
    • C. 7
    • D. 8
    • Discuss


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