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Chi Square 17 October
1. 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
2. Business Mathematics
Dr. T.K. Jain.
AFTERSCHOOOL
Centre for social entrepreneurship
Bikaner
M: 9414430763
tkjainbkn@yahoo.co.in
www.afterschool.tk
www.afterschoool.tk
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
3. 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).
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
4. 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).
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
5. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
6. 3 persons have 8 seats for them. In
how many ways can they occupy
these?
8p3 (because order is important here, so
use permutation).
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
7. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
8. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
9. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
10. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
11. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
12. 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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
13. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
14. In how many ways can I make a
necklace from 9 jewels that I have ?
Formulae = (n-1)! / 2
=8!/2
=20160 answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
15. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
16. ABOUT AFTERSCHOOOL
Afterschoool conducts three year integrated PGPSE (after
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
social entrepreneurship in schools and colleges all over India –
start social entrepreneurship club in your institution today with
the help from afterschoool and help us in developing society.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
17. 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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
18. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
19. 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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
20. 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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
21. Flexible Specialisations:
Spiritualising business and society
Rural development and transformation
HRD and Education, Social Development
NGO and voluntary work
Investment analysis,microfinance and inclusion
Retail sector, BPO, KPO
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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
22. 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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
23. 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)
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
24. 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
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
25. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
26. 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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
27. 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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS