4 August 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

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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).

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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). 

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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.

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3 persons have 8 seats for them. In how many ways can they occupy these?  8p3

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

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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.

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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.

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In how many ways can we set 10 examination papers so that the best and the worst paper never come together? 1. 2.

3. 4.

We have total 10! But best and worst cannot come 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. Answer: 10! – (9!*2)=2903040

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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. MATERIAL FOR PGPSE PARTICIPANTS www.afterschoool.tk AFTERSCHOOOL

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. 

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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 

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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.

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

= (n-1)! / 2

 =8!/2  =20160

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answer.

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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

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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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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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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

www.afterschoool.tk social entrepreneurship for better society

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS