Management- Business Mathematics 1. Permutations 2. Combination 3. Circular permutation 4. Permutation with restriction 5. Combination with restriction 6. Principle of Mathematical induction

1. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Affiliated Institution of G.G.S.IP.U, Delhi
Business Mathematics
Paper Id 17105
Paper code BBA 105

2. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
SCOPE OF BUSINESS
MATHEMATICS
• Business Mathematics is an important subject
and knowledge of it enhances a person's
reasoning and problem-solving skills.
• It aims at equipping student with a broad based
knowledge of mathematics with emphasis on
business applications.

3. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
It is recognised that the use of Mathematics
(with the help of algorithms and mathematical
rules) in the R&D adds billions of pounds
value to the businesses all over the world.

4. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Course Contents: UNIT -1
• Permutations
• Combination
• Circular permutation
• Permutation with restriction
• Combination with restriction
• Principle of Mathematical induction
• A.P & G.P

5. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Permutation
Permutation is the ordered arrangement of all
or part of a set of objects .
More precisely ,an ordered arrangement of r
objects chosen from n distinct objects is called
Permutation of n objects taken r at a time.
nPr
= n ‫إ‬
(n-r) ‫إ‬

6. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
REPEATED PERMUTATION
The number of distinct permutations of n
objects of which n1 of one kind ,n2 of second
kind,……….,nk of kth kind ,is given by
n‫إ‬
n1 ‫إ‬ × n2 ‫إ‬ ×…… nk ‫إ‬

7. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Question
Ques. Find the number of distinct
permutations of the letters of the word
MATHEMATICS.

8. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Question
Ques. In how many ways can the letters of
the word“ACCOUNTANT”be arranged?

9. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Ques. In how many ways can the letters of the
word STRANGE be arranged so that
(i) The vowels are never seperated
(ii) The vowels never come together
RESTRICTED PERMUTATION

10. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
CIRCULAR PERMUTATION
The number of circular permutation of n
distinct objects is (n-1)‫إ‬
For example: The number of ways in which 5
persons be seated at around table conference is
(5-1)‫إ‬ = 4‫إ‬
= 24

11. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
Combination
A selection of ‘r’ objects ,neglecting the order of
Selection ,from ‘n’ distinct objects is called a
Combination of n objects taken r at a time.
nCr
= n ‫إ‬
(n-r)‫إ‬ r‫إ‬
nPr
= r ‫إ‬ . nCr

12. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
QUESTION
QUES.A box contains 7 red,6 white and 4 blue
balls .How many selections of three balls can
be made so that:
(i) none is red
(ii) one is of each colour

13. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75
QUESTION
Ques. In how many ways can a committee of 8
be chosen from 12 socialists and 9
conservatives to give a socialist majority if
atleast 2 conservatives are included?

14. TRINITY INSTITUTE OF PROFESSIONAL STUDIES
Sector – 9, Dwarka Institutional Area, New Delhi-75