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 1^st 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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