Aptitude Questions: Permutations & Combinations Set 1

Hello Aspirants. Welcome to Online Reasoning Section in AffairsCloud.com. Here we are creating question sample in coded Permutations & Combinations, which is common for all the  competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

  1. In a exam paper 1st section contains 10 questions each with 5 choices and  second section contains 5 questions each with 4 choices. In how many different ways can the paper be answered if all the questions are attempted.
    A.105 × 45
    B.510 × 45
    C.510 × 54
    D.105 × 54
    E.None of these
    Answer & Explanation
    Answer – B. 510 × 45
    Explanation :
    10 questions with 5 choices = 510
    20 questions with 4 choices =  45
  2. How many four digit number can be formed with the digits 5,9,1 and 3 only ?
    A.64
    B.216
    C.256
    D.324
    E.None of these
    Answer & Explanation
    Answer – C.256
    Explanation :
    4*4*4*4 = 256
  3. Find the number of ways in which 9 students equally divided into three groups ?
    A.280
    B.360
    C.200
    D.540
    E.None of these
    Answer & Explanation
    Answer – A.280
    Explanation :
    9!/[3! ×(3!)3] = 362880/6*216 = 280
  4. Find the number of ways of distributing 9 identical balls into 4 boxes so that no box is empty and each box being large enough to accommodate all balls ?
    A.63
    B.45
    C.62
    D.56
    E.None of these
    Answer & Explanation
    Answer – D.56
    Explanation :
    9-1 C 4-1  = 8 C 3 = 8*7*6/3*2*1 = 56
  5. 12 students participated in  the competition and each get different score. In how many ways can three different prizes given ?
    A.1320
    B.1240
    C.1650
    D.1870
    E.None of these
    Answer & Explanation
    Answer – A.1320
    Explanation :
    12*11*10 = 1320
  6. How many arrangement can be made from the word COMMERCE, such that all the vowels do not come together ?
    A.6800
    B.5600
    C.1080
    D.9000
    E.None of these
    Answer & Explanation
    Answer – D.9000
    Explanation :
    8 letters = 8!/ 2! 2! = 40320/4 = 10080
    6 letters = 6!/2! = 360
    Vowels = 3!/2! =  3
    No of ways vowels together = 360*3 = 1080
    No of ways vowels not together = 10080 – 1080 = 9000
  7. Three brothers have 5 shirts, 8 pants and 6 ties. In how many ways can they wear them ?
    A.2400200
    B.2419000
    C.2419200
    D.2419100
    E.None of these
    Answer & Explanation
    Answer – C. 2419200
    Explanation :
    5 P 3 *8 P 3*  6 P 3  = 60*336*120 = 2419200
  8. 5 men and 3 women are to be seated such that no 2 women sit together and  2 men sit together. Find the no of ways in which this can be arranged ?
    A.625
    B.720
    C.525
    D.516
    E.None of these
    Answer & Explanation
    Answer – B.720
    Explanation :
    5!*3! = 120*6 = 720
  9. A group consists of 3 couples  in which each of the 3 men have one wife each. In how many ways could they arranged in a straight line so that the men and women occupy alternate position ?
    A.216
    B.125
    C.256
    D.72
    E.None of these
    Answer & Explanation
    Answer – D.72
    Explanation :
    3!*3! + 3!*3! = 36+36 = 72
  10. In how many ways can 5 different balls be distributed to 4 different boxes, when each of the can hold any no of ball ?
    A.1024
    B.1200
    C.1234
    D.1600
    E.None of these
    Answer & Explanation
    Answer – A.1024
    Explanation :
    No of way =45  = 1024

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