8/14/2019 30 July Business Mathematics
1/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
BUSINESS MATHEMATICS
AFTERSCHOOOL DEVELOPING CHANGEMAKERS
CENTRE FOR SOCIAL ENTREPRENEURSHIP
PGPSE PROGRAMME
World Most Comprehensive programme in socialentrepreneurship & spiritual entrepreneurship
OPEN FOR ALL FREE FOR ALL
8/14/2019 30 July Business Mathematics
2/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
BUSINESS MATHEMATICS
Dr. T.K. Jain.
AFTERSCHOOOL
Centre for social entrepreneurship
Bikaner
M: 9414430763
www.afterschool.tk
www.afterschoool.tk
http://www.afterschool.tk/http://www.afterschoool.tk/http://www.afterschoool.tk/http://www.afterschool.tk/8/14/2019 30 July Business Mathematics
3/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
WE HAVE ONE TABLE, 1CHAIR, 1
SUITCASE, 1 BAT, 1 WEIGHING
MACHINE, AND 1 GUITAR. IN HOW
MANY WAYS CAN WE SELECT ONE
OR ALL OF THEM?
We have6 items.Formulae : 2^n -1.
=2^6-1
=64-1=63 answer.
8/14/2019 30 July Business Mathematics
4/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
How many 3 digit numbers can we
from from 1,2,3,4,5,6, (repeatition
allowed)?For first digit we have 6 choices, for
second digit we have again 6 choices,
for third digit again we have 6 choices.Answer : 6*6*6 =216 answer.
8/14/2019 30 July Business Mathematics
5/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
We have 7 red, 6 white, 4 blue balls.
We have to select 3 balls. How can
we select so that we have all 3 redballs?
We have 7c3 choices (3 red balls out of
7 balls).7!/ (3! * 4!)
=35 ways to select 3 red balls.
8/14/2019 30 July Business Mathematics
6/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
We have 7 red, 6 white, 4 blue balls.
We have to select 3 balls. How can
we select so that we have one ofeach colour?
Now we have 7c1 * 6c1 * 4c1.
Thus we have 7*6*4 = 168 answer.
8/14/2019 30 July Business Mathematics
7/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
We have 7 red, 6 white, 4 blue balls.
We have to select 3 balls. How can
we select so that we dont have anyred ball?
There are total 17 balls, out of which 7
are red balls. Thus we have only 10 balls
to choose from.
Thus we have 10 c 3 as our answer.
10! / (7! * 3!)
= 120 answer.
8/14/2019 30 July Business Mathematics
8/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
We have 8 points. No 3 points are on
the same line. How many triangles
can we form from these 8 points?Solution: 8c3
8! / (5! * 3!)
=56 answer.
8/14/2019 30 July Business Mathematics
9/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
Find the number of ways in which
you can organise the word CRITICAL
so that vowels always occupy odd
positions?
We have 3 vowels. We have 8 positions,
so 4 are available for vowels. Thus wecan take 3 vowels and one consonant for
these 4 odd positions. Remaining 4
positions can be filled by remaining 4
consonants. But there are repeatitions.
Divide for repeatitions. 4!/2! * 4!/2! = 12*
12 = 144 answer.
8/14/2019 30 July Business Mathematics
10/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
In how many ways can we arrange
presentations of Nidhi, Hulash,
Rishabh and Tarachand? Tarachandwants to give presentation before
Hulash?
We have 4 speakers. They can be arranged
in 4! Or 24 ways. But in some of the casesTarachand will be behind Hulash, we haveto remove those cases. Let us keepTarachand just behind Hulash and rotateothers, we have 3! = 6 cases. Let us
consider Tarachand with a gap of 1 place.We have 2 cases. We have one case whenthere is a gap of 2 between Tarachand andHulash. Thus we have 24-9 = 15 cases.Answer.
8/14/2019 30 July Business Mathematics
11/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
There are 5 speakers, A,B,C,D,E. A
will speak just before B. in how
many ways can they speak?Let us take A & B together.
We have 4 speakers AB, C,D,E.
Thus we have 4! = 24 answer.
8/14/2019 30 July Business Mathematics
12/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
There are 5 speakers, A,B,C,D,E. A
will speak before B. in how many
ways can they speak? We have 5! = 120 ways. However, we have to
remove all such cases where B is speakingbefore A. There are many such cases. Let us take
BA as one combination. We have 24 ways withBA. Let us take B-A (one gap), we have differentcombinations like B-A- - or b-a- or - - b-a, thuswe have 18 such options. We can have 2 gapsbetween B & A. which can be B - - A- or B - - A.
thus we have 12 such options. We can have 3gaps between B & A and there are 6 suchoptions. Thus answer is 120 (24+18+12+6) = 60answer.
8/14/2019 30 July Business Mathematics
13/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
There are 12 points on a plane of
which 5 are collinear. How many
triangles can we make?We have to select 3 points from 12
points, but these 3 points should not becollinear. Thus we have to remove allsuch cases where points are collinear.
12c 3 5c312*11*10/3*2*1 5*4/2*1=220 10=210 answer.
8/14/2019 30 July Business Mathematics
14/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
How many straight lines can we
form from 16 points on a plane?We have to select 2 points from 16
points.
16 c216! / (14! * 2!)
16*15 / 2*1
=8*15
=120 answer.
8/14/2019 30 July Business Mathematics
15/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
NPR = 336 and NCR = 56, N & R
will be what? Options: 3,2 b. 8,3, c. 7,4 Let us try with option B. 8P3 = 8*7*6 = 336 8C3 = 8*7*6/3*2*1 = 56 Thus option B gives correct answer. ANOTHER METHOD: NCR * R! = NPR 56 *R! = 336; R! = 6 R =3. (which is there in option B only).
8/14/2019 30 July Business Mathematics
16/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
10pr = 604800 and 10cr = 120,
what is value of R?NCR * R! = NPR
120 * R! = 604800
R! = 5040R = 7 answer.
8/14/2019 30 July Business Mathematics
17/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
THERE ARE 5 CANDIDATES AND 3
MEMBERS TO BE ELECTED. IN HOW
MANY WAYS CAN A VOTER VOTE?
The voter has a choice, he may give 1 vote,2 vote or 3 votes. He has 5 choices in eachcase.
If he gives one vote, his choice is 5c1, if hegives 2 votes, his choices are 5c2, if hegives 3 votes, his choices are 5c3.
Thus his total choices are 5 + 10+10=25
answer. We have not taken a situation when he
doesnot vote at all.
8/14/2019 30 July Business Mathematics
18/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
The number of ways in which 12
students may be equally divided in 3
groups?
We have to take a group of 4 persons
each. For selecting first group, we have
12 persons and we have to take 4, so12c4 is the combination.
Thus we have to select: (12c4 * 8c4 *
4c4)/ 3!Thus we have 5775 answer
8/14/2019 30 July Business Mathematics
19/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
ABOUT A FTERSCH OOOLAfterschoool 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 forCS / CFP / CFA /CMA / FRM. This
course is also available online also. It also conductsworkshops 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.
8/14/2019 30 July Business Mathematics
20/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
Why such a programme?
To promote people to take up entrepreneurship
and help develop the society
To enable people to take up franchising andother 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
8/14/2019 30 July Business Mathematics
21/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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.
8/14/2019 30 July Business Mathematics
22/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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
8/14/2019 30 July Business Mathematics
23/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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
8/14/2019 30 July Business Mathematics
24/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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
8/14/2019 30 July Business Mathematics
25/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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 weekendclasses
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 studymaterial
8/14/2019 30 July Business Mathematics
26/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
Components
Pedagogy curriculum and approach based on IIM Ahmedabad and ISBHyderabad (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)
8/14/2019 30 July Business Mathematics
27/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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
8/14/2019 30 July Business Mathematics
28/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
Branches
AFTERSCHOOOL will shortly open itsbranches in important cities in Indiaincluding Delhi, Kota, Mumbai, Gurgaonand other important cities.Afterschooolians will be responsible formanaging and developing these
branches and for promoting socialentrepreneurs.
8/14/2019 30 July Business Mathematics
29/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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.
8/14/2019 30 July Business Mathematics
30/31
www.afterschoool.tk AFTERSCHOOOL MATERIAL FO
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 yourselfonly
http://www.afterschoool.tk/8/14/2019 30 July Business Mathematics
31/31
www afterschoool tk AFTERSCHOOOL MATERIAL FO
www.afterschoool.tk
social entrepreneurship for better
society
http://www.afterschoool.tk/http://www.afterschoool.tk/