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

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

The document PPT - Permutations and Combinations Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation is a part of the CA Foundation Course Business Mathematics and Logical Reasoning & Statistics.
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``` 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
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## Business Mathematics and Logical Reasoning & Statistics

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