30 July Business Mathematics

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

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BUSINESS MATHEMATICS Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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. www.afterschoool.tk

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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.

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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 red balls?  We

have 7c3 choices (3 red balls out of 7 balls).  7!/ (3! * 4!)  =35 ways to select 3 red balls.

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We have 7 red, 6 white, 4 blue balls. We have to select 3 balls. How can we select so that we have one of each colour?  Now

we have 7c1 * 6c1 * 4c1.  Thus we have 7*6*4 = 168 answer.

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We have 7 red, 6 white, 4 blue balls. We have to select 3 balls. How can we select so that we don’t have any red 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. www.afterschoool.tk

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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.

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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 we can 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.

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In how many ways can we arrange presentations of Nidhi, Hulash, Rishabh and Tarachand? Tarachand wants to give presentation before Hulash? 

We have 4 speakers. They can be arranged in 4! Or 24 ways. But in some of the cases Tarachand will be behind Hulash, we have to remove those cases. Let us keep Tarachand just behind Hulash and rotate others, we have 3! = 6 cases. Let us consider Tarachand with a gap of 1 place. We have 2 cases. We have one case when there is a gap of 2 between Tarachand and Hulash. Thus we have 24-9 = 15 cases. Answer. www.afterschoool.tk

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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.

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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 speaking before A. There are many such cases. Let us take BA as one combination. We have 24 ways with BA. Let us take B-A (one gap), we have different combinations like B-A- - or –b-a- or - - b-a, thus we have 18 such options. We can have 2 gaps between B & A. which can be B - - A- or – B - - A. thus we have 12 such options. We can have 3 gaps between B & A and there are 6 such options. Thus answer is 120 – (24+18+12+6) = 60 answer.

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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 be collinear. Thus we have to remove all such cases where points are collinear.  12c 3 – 5c3  12*11*10/3*2*1 – 5*4/2*1  =220 – 10  =210 answer. www.afterschoool.tk

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How many straight lines can we form from 16 points on a plane?  We

have to select 2 points from 16 points.  16 c2  16! / (14! * 2!)  16*15 / 2*1  =8*15  =120 answer. www.afterschoool.tk

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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).

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10pr = 604800 and 10cr = 120, what is value of R?  NCR

* R! = NPR  120 * R! = 604800  R! = 5040  R = 7 answer.

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THERE ARE 5 CANDIDATES AND 3 MEMBERS TO BE ELECTED. IN HOW MANY WAYS CAN A VOTER VOTE? 

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The voter has a choice, he may give 1 vote, 2 vote or 3 votes. He has 5 choices in each case. If he gives one vote, his choice is 5c1, if he gives 2 votes, his choices are 5c2, if he gives 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.

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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, so 12c4 is the combination.  Thus we have to select: (12c4 * 8c4 * 4c4)/ 3!  Thus we have 5775 answer

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ABO UT A FTERSCH OOO L 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.

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Why such a programme? 

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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

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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.

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About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs     

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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

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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

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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

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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 www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS 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)

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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

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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.

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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.

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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

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www.afterschoool.tk social entrepreneurship for better society

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