MCQ - Permutations and Combinations Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation

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CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
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CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Sol : The word DRAUGHT consists of 7 letters of which 5 are    
consonants and two are vowels. Two Vowels should not be seperated.   
   2 vowels= 1 unit=     2! ? 2 ways-----(1)  
 remaning units=7-2+1=6 .the total number of ways of arranging them is  
6p6 = 6! = 720 ways.----(2) 
               The total number of arrangements of word DRAUGHT  
                   are(1)x(2)=2x720=1440 ways 
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CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Sol : The word DRAUGHT consists of 7 letters of which 5 are    
consonants and two are vowels. Two Vowels should not be seperated.   
   2 vowels= 1 unit=     2! ? 2 ways-----(1)  
 remaning units=7-2+1=6 .the total number of ways of arranging them is  
6p6 = 6! = 720 ways.----(2) 
               The total number of arrangements of word DRAUGHT  
                   are(1)x(2)=2x720=1440 ways 
SOL: 6 economics books can be arranged among themselves 
in 6! Ways---(1),3 mathematics books can be arranged in 3! 
Ways –(2)and the 2 books on accountancy can be arranged  
In 2! Ways—(3). 
      . Now there are three units. These 3 units can be arranged 
in 3! Ways.----(4) 
            Total number of arrangements 
          (1)x(2)x(3)x(4)=3!x6!x3!x2!ways. 
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CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Sol : The word DRAUGHT consists of 7 letters of which 5 are    
consonants and two are vowels. Two Vowels should not be seperated.   
   2 vowels= 1 unit=     2! ? 2 ways-----(1)  
 remaning units=7-2+1=6 .the total number of ways of arranging them is  
6p6 = 6! = 720 ways.----(2) 
               The total number of arrangements of word DRAUGHT  
                   are(1)x(2)=2x720=1440 ways 
SOL: 6 economics books can be arranged among themselves 
in 6! Ways---(1),3 mathematics books can be arranged in 3! 
Ways –(2)and the 2 books on accountancy can be arranged  
In 2! Ways—(3). 
      . Now there are three units. These 3 units can be arranged 
in 3! Ways.----(4) 
            Total number of arrangements 
          (1)x(2)x(3)x(4)=3!x6!x3!x2!ways. 
SOL: (i) consider the 3 sisters as 1 unit =3!ways-----(1)                              . 
 total units=7-3+1= 5 units which can be arranged  in 5! Ways----(2) .  . 
          there fore total number of ways in which all the sisters sit 
together=(1)x(2) =5!x3!=720 ways                                                
(ii) 4brothers are aranged 4!ways-----(1)In this case,each sister must sit on 
each side of the brothers. In between 4 brothers there  are 5  positions 
   as indicated below by upward arrow 
 
                                              B1          B2          B3        B4   
  3 sisters can sit in the 5 places in 5p3 ways.----(2) 
Total number of ways =(1)x(2) 
4!x5p3=60x24=1,440 
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CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Sol : The word DRAUGHT consists of 7 letters of which 5 are    
consonants and two are vowels. Two Vowels should not be seperated.   
   2 vowels= 1 unit=     2! ? 2 ways-----(1)  
 remaning units=7-2+1=6 .the total number of ways of arranging them is  
6p6 = 6! = 720 ways.----(2) 
               The total number of arrangements of word DRAUGHT  
                   are(1)x(2)=2x720=1440 ways 
SOL: 6 economics books can be arranged among themselves 
in 6! Ways---(1),3 mathematics books can be arranged in 3! 
Ways –(2)and the 2 books on accountancy can be arranged  
In 2! Ways—(3). 
      . Now there are three units. These 3 units can be arranged 
in 3! Ways.----(4) 
            Total number of arrangements 
          (1)x(2)x(3)x(4)=3!x6!x3!x2!ways. 
SOL: (i) consider the 3 sisters as 1 unit =3!ways-----(1)                              . 
 total units=7-3+1= 5 units which can be arranged  in 5! Ways----(2) .  . 
          there fore total number of ways in which all the sisters sit 
together=(1)x(2) =5!x3!=720 ways                                                
(ii) 4brothers are aranged 4!ways-----(1)In this case,each sister must sit on 
each side of the brothers. In between 4 brothers there  are 5  positions 
   as indicated below by upward arrow 
 
                                              B1          B2          B3        B4   
  3 sisters can sit in the 5 places in 5p3 ways.----(2) 
Total number of ways =(1)x(2) 
4!x5p3=60x24=1,440 
Sol: suppose that we have 11 chairs in a row and we want the 6 boys and 
5 girls to be seated such that no two girls and no two boys are together. If 
we number the chairs from left to right,the arrangements will be possible if 
and only if boys occupy the odd places and girls occupy the even places 
in the row. 
The six odd places from 1 to 11 may filled in by 6 boys in 6p6 ways.---(1) 
Similarly, the five even 
Places from 2 to 10 may be filled in by 5 girls in 5p5 ways.---(2) 
Hence, by the fundamental principle, the total number of required 
arrangements  
                     ?(1)x(2)= 6p6 x 5p5 = 6! X 5! = 720x120 = 86400