Aptitude Questions: Permutations & Combinations Set 3

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 how many ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes ?
   A.1234
   B.1728
   C.5314
   D.1331
   E.None of these
   

   Answer & Explanation

   Answer – B.1728
   Explanation :
   12^3 = 1728
   
   
   
2. Total no of ways in which 30 sweets can be distributed among 6 persons ?
   A.35 C ₅
   B.36 C ₅
   C.36 C ₆
   D.35!/5!
   E.None of these
   

   Answer & Explanation

   Answer – A. ³⁵ C ₅
   Explanation :
   ^30+6-1 C _6-1 = ³⁵ C ₅
   
   
   
3. A bag contains 4 red balls and 5 black balls. In how many ways can i make a selection so as to take atleast 1 red ball and 1 black ball ?
   A.564
   B.345
   C.465
   D.240
   E.None of these
   

   Answer & Explanation

   Answer – C.465
   Explanation :
   2 ⁴-1 = 16 -1 = 15
   2 ^5-1 = 32 -1 = 31
   15*31 = 465
   
   
   
4. In how many ways can 7 beads be strung into necklace ?
   A.2520
   B.5040
   C.720
   D.360
   E.None of these
   

   Answer & Explanation

   Answer – D.360
   Explanation :
   No of way in Necklace = (n-1)!/2 = 6!/2
   = 720/2 = 360
   
   
   
5. Find the no of 3 digit numbers such that  atleast one of the digit is 6 (with repetitions) ?
   A.252
   B.345
   C.648
   D.560
   E.None of these
   

   Answer & Explanation

   Answer – A.252
   Explanation :
   Total no of 3 digit number = 9*10*10 = 900
   No of 3 digit number- none of the digit is 6 = 8*9*9 = 648
   No of 3 digit number – atleast one digit is 6 = 900-648 = 252
   
   
   
6. In how many ways  can 7 girls and 4 boys stand in a row so that no 2 boys are together ?
   A.8467200
   B.9062700
   C.7407000
   D.8407200
   E.None of these
   

   Answer & Explanation

   Answer – A. 8467200
   Explanation :
   No of ways = 7!*⁸P₄
   7! = 5040
   8P4 = 8*7*6*5 = 1680
   No of ways = 5040*1680 = 8467200
   
   
   
7. In how many ways the letters of the word PERMUTATION be arranged ?
   A.10!/2!
   B.10!
   C.11!
   D.11!/2!
   E.None of these
   

   Answer & Explanation

   Answer – D. 11!/2!
   Explanation :
   No of ways = 11!/2!
   
   
   
8. How many numbers can be formed with the digits 1, 7, 2, 5 without repetition ?
   A.89
   B.56
   C.64
   D.72
   E.None of these
   

   Answer & Explanation

   Answer – C.64
   Explanation :
   1 digit number = 4
   2 digit no = 4*3 = 12
   3 digit no = 4*3*2 = 24
   4 digit no = 4*3*2*1 = 24
   Total = 4+12+24+24 = 64
   
   
   
9. There are 3 boxes and 6 balls. In how many ways these balls can be distributed if all the balls and all the boxes are different?
   A.243
   B.512
   C.729
   D.416
   E.None of these
   

   Answer & Explanation

   Answer – C.729
   Explanation : 3^6 = 729
   
   
   
10. In how many ways can 4 books be selected out of 10 books on different subjects ?
    A.210
    B.320
    C.716
    D.5040
    E.None of these
    

    Answer & Explanation

    Answer – A.210
    Explanation :
    ¹⁶C₄  =  10*9*8*7/4*3*2*1 = 5040/24 = 210
    
    
    

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