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

 Page 1


CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Page 2


CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Selecting smaller or  equal number of persons or objects 
and the importance is given to the arrangement or order 
in which the objects are placed is called permutations. 
Therefore out of ‘n’ things if ‘r’ things are arranged then 
the number of arrangements is called as permutations. 
np
r 
=    n!/(n-r)! =n(n-1)(n-2)…(n-r+1)                            
5p
3
=5!/(5-3)!=5x4x3=60                  
Page 3


CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Selecting smaller or  equal number of persons or objects 
and the importance is given to the arrangement or order 
in which the objects are placed is called permutations. 
Therefore out of ‘n’ things if ‘r’ things are arranged then 
the number of arrangements is called as permutations. 
np
r 
=    n!/(n-r)! =n(n-1)(n-2)…(n-r+1)                            
5p
3
=5!/(5-3)!=5x4x3=60                  
                                   
                               
1. np
r 
+ r.np
r-1
 = n+1p
r 
2. Sum of all ‘r’ digits numbers [1 to 9], excluding 0 is             
n-1p
r-1
 x(sum of digits) x 111…..r times.   
3. Sum of all ‘r’ digit numbers including ‘0’ is 
4. Sum [n-1pr-1 x 111…..r times – n-2pr-2 x        
111…(r-1)times] 
Page 4


CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Selecting smaller or  equal number of persons or objects 
and the importance is given to the arrangement or order 
in which the objects are placed is called permutations. 
Therefore out of ‘n’ things if ‘r’ things are arranged then 
the number of arrangements is called as permutations. 
np
r 
=    n!/(n-r)! =n(n-1)(n-2)…(n-r+1)                            
5p
3
=5!/(5-3)!=5x4x3=60                  
                                   
                               
1. np
r 
+ r.np
r-1
 = n+1p
r 
2. Sum of all ‘r’ digits numbers [1 to 9], excluding 0 is             
n-1p
r-1
 x(sum of digits) x 111…..r times.   
3. Sum of all ‘r’ digit numbers including ‘0’ is 
4. Sum [n-1pr-1 x 111…..r times – n-2pr-2 x        
111…(r-1)times] 
np
n
 = n! 
np
1 
= n 
np
0
 = 1 
0!  = 1 
np
r 
= n.(n-1)p(r-1)   
Page 5


CPT Section D Quantitative Aptitude Chapter 5 
Preethi Rathi 
 
Selecting smaller or  equal number of persons or objects 
and the importance is given to the arrangement or order 
in which the objects are placed is called permutations. 
Therefore out of ‘n’ things if ‘r’ things are arranged then 
the number of arrangements is called as permutations. 
np
r 
=    n!/(n-r)! =n(n-1)(n-2)…(n-r+1)                            
5p
3
=5!/(5-3)!=5x4x3=60                  
                                   
                               
1. np
r 
+ r.np
r-1
 = n+1p
r 
2. Sum of all ‘r’ digits numbers [1 to 9], excluding 0 is             
n-1p
r-1
 x(sum of digits) x 111…..r times.   
3. Sum of all ‘r’ digit numbers including ‘0’ is 
4. Sum [n-1pr-1 x 111…..r times – n-2pr-2 x        
111…(r-1)times] 
np
n
 = n! 
np
1 
= n 
np
0
 = 1 
0!  = 1 
np
r 
= n.(n-1)p(r-1)   
Divisibility  by 2: 
A numeric number is divisible by 2 if the last digit i.e., the digits 
in the units place is either even or zero. 
Divisibility by 3: 
A number is divisible by 3 if the sum of the digits is multiple 
of 3