Chi Square 17 October

Business Mathematics

AFTERSCHOOOL – DEVELOPING CHANGE
MAKERS
CENTRE FOR SOCIAL ENTREPRENEURSHIP
PGPSE PROGRAMME –
World’ Most Comprehensive programme in social
entrepreneurship & spiritual entrepreneurship
OPEN FOR ALL FREE FOR ALL

www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Business Mathematics
Dr. T.K. Jain.
AFTERSCHOOOL
Centre for social entrepreneurship
Bikaner
M: 9414430763
tkjainbkn@yahoo.co.in
www.afterschool.tk
www.afterschoool.tk


You have 8 routes to go from your
home to office. How many choices do
you have to go and return (you don’t
use same route while returning)?

8*7


=56 (because you don’t use same route

while returning, so choices are not 8 but
7).


You have 8 routes to go from your
home to office. How many choices do
you have to go and return (you use
same route while returning)?

8 answer


(because you don’t have choice while

returning).


How many telephone connections
can be alloted from 8 numbers – from
0 to 9?

You can use a number again and again

– for example a number can be
11111111.
Thus you have 10 choices for each of

the 8 digits.
Thus 10^8 is the answer.



3 persons have 8 seats for them. In
how many ways can they occupy
these?

8p3 (because order is important here, so

use permutation).


How many 4 digit numbers greater
than 7000 can be formed out of
3,4,7,8,9?

You have 3 choices for first digit (7,8,9)


You have now (5-1) = 4 choices for 2nd

digit, you have 3 choices for 3rd digit, you
have 2 choices for 4th digit.
Thus : 3*4*3*2 = 72 answer.



In how many ways can we arrange 5
books of OB, 3 of Mgmt and 3 of Law,
if books of one subject are always
together?

There are 3 subjects, so we have 3!.


Books of one subject can be

interchanged easily. Thus we have 5!*3!
*3!
=3!*5!*3!*3! =25920 Answer.



In how many ways can we set 10
examination papers so that the best
and the worst paper never come
together?

We have total 10!
1.
But best and worst cannot come
2.
together, let us treat them as one and
find the cases when they come
together. Thus we have (10-1)!*2
Remove step 2 from step 1.
3.
Answer: 10! – (9!*2)=2903040
4.


We organise a group discussion at
AFTERSCHOOOL, where 15 students
participate. Two particular students
always sit together. In how many
ways can they sit for GD?

Two students are always together, so let

us treat them as one. We have 14
students now.
(N-1)!. Thus 13 factorial. However, 2

students can exchange seats among
themselves, so we have 13! * 2 answer.
=12454041600 ans.


How many 4 digit words can be
made from Mathematics?
We have 11 digits.

We have repeatition of A, T, M.

Thus we have 8 digits. We have choices

like all different digits, or 2 common and 2
different digits or 2 pairs.
All different : 8p4 = 1680

1 pair and 3 different digits: 3p1 *7p2 =

126 *3! =756
2 pairs from 3 = 3p2 = 6 *3 = 18

Total =2454 answer.



How many ways 4 digits may be
selected from Mathematics?
We have 11 digits.

We have repeatition of A, T, M.

Thus we have 8 digits. We have choices

like all different digits, or 2 common and 2
different digits or 2 pairs.
All different : 8c4 = 70

1 pair and 3 different digits: 3c1 *7c2 =63

2 pairs from 3 = 3c2 = 3

Total = 136



In how many ways can 9 students sit
on a bench to be photographed, if 2
particular students want to sit at
corner positions only?

Corner positions are occupied, so we

have 7 positions left. We have 7!. The
corner positions can be changed.
Thus answer is 7! * 2


= 10080 answer.



In how many ways can I make a
necklace from 9 jewels that I have ?

Formulae = (n-1)! / 2


=8!/2


=20160 answer.



A boat’s crew consist of 8 men, 3 of
whom can row only on one side and 2
only on the other. The number of
ways in which the crew can be
arranged is ?

We have to take equal number of persons on

both the sides of the boat. Thus we have to
take 4 persons on each side. We have 4
seats on both sides. Thus we have total 4!
Choices on one side, thus total number of
choices are 4!*4! (with 3 on one side and 2
on other). However, we have 3 persons who
can sit on either side. So let us multiply 576
*3, we get 1728. answer.

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class 12th along with IAS / CA / CS) and 18 month PGPSE
(Post Graduate Programme in Social Entrepreneurship) along
with preparation for CS / CFP / CFA /CMA / FRM. This course
is also available online also. It also conducts workshops on
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start social entrepreneurship club in your institution today with
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Why such a programme?
To promote people to take up entrepreneurship

and help develop the society
To enable people to take up franchising and

other such options to start a business / social
development project
To enable people to take up social development

as their mission
To enable people to promote spirituality and

positive thinking in the world


Who are our supporters?
Afterschoolians, our past beneficiaries,

entrepreneurs and social entrepreneurs
are supporting us.
You can also support us – not

necessarily by money – but by being
promotor of our concept and our ideas.


About AFTERSCHOOOL PGPSE – the best
programme for developing great entrepreneurs

Most flexible, adaptive but rigorous programme


Available in distance learning mode


Case study focused- latest cases


Industry oriented practical curriculum


Designed to make you entrepreneurs – not just

an employee
Option to take up part time job – so earn while

you learn
The only absolutely free course on internet



Workshops from
AFTERSCHOOOL
IIF, Delhi

CIPS, Jaipur

ICSI Hyderabad Branch

Gyan Vihar, Jaipur

Apex Institute of Management, Jaipur

Aravali Institute of Management, Jodhpur

Xavier Institute of Management, Bhubaneshwar

Pacific Institute, Udaipur

Engineering College, Hyderabad



Flexible Specialisations:
Spiritualising business and society

Rural development and transformation

HRD and Education, Social Development
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NGO and voluntary work
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Investment analysis,microfinance and inclusion

Retail sector, BPO, KPO
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Accounting & Information system (with CA / CS /CMA)

Hospital management and Health care

Hospitality sector and culture and heritage

Other sectors of high growth, high technology and social

relevance


Salient features:
The only programme of its kind (in the whole world)

 No publicity and low profile course
 For those who want to achieve success in life – not just a
degree
 Indepth knowledge and expertise
 Professional approac: World class approach
 Strong intellectual and business capabilities
 Flexible – you may stay for a month and continue the rest of
the education by distance mode. / you may attend weekend
classes
 Scholarships for those from poor economic background
 Latest and constantly changing curriculum – keeping pace
with the time
 Placement for those who are interested
 Admissions open throughout the year
 Latest and most advanced technologies, books and study
material

Components
Pedagogy curriculum and approach based on IIM Ahmedabad and ISB

Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad)
Meditation, spiritualisation, and self development

Essential softwares for business

Business plan, Research projects

Participation in conferences / seminars

Workshops on leadership, team building etc.

Written submissions of research projects/articles / papers

Interview of entrepreneurs, writing biographies of entrepreneurs

Editing of journals / newsletters

Consultancy / research projects

Assignments, communication skill workshops

Participation in conferences and seminars

Group discussions, mock interviews, self development diaryng

Mind Power Training & writing workshop (by Dr. T.K.Jain)



Pedagogy
Case analysis,

Articles from Harvard Business Review

Quiz, seminars, workshops, games,

Visits to entrepreneurs and industrial visits

Presentations, Latest audio-visuals

Group discussions and group projects

Periodic self assessment

Mentoring and counselling

Study exchange programme (with institutions out of India)

Rural development / Social welfare projects



Branches
AFTERSCHOOOL will shortly open its

branches in important cities in India
including Delhi, Kota, Mumbai, Gurgaon
and other important cities.
Afterschooolians will be responsible for
managing and developing these
branches – and for promoting social
entrepreneurs.


Case Studies
We want to write case studies on social

entrepreneurs, first generation
entrepreneurs, ethical entrepreneurs.
Please help us in this process. Help us
to be in touch with entrepreneurs, so that
we may develop entrepreneurs.


Basic values at afterschoool
Share to learn more

Interact to develop yourself

Fear is your worst enemy

Make mistakes to learn

Study & discuss in a group

Criticism is the healthy route to mutual support

and help
Ask fundamental questions : why, when, how &

where?
Embrace change – and compete with yourself

only

www.afterschoool.tk
social entrepreneurship for better
society


Chi Square 17 October

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Chi Square 17 October