5 August Business mathematics by afterschool

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									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 tkjainbkn@yahoo.co.in www.afterschool.tk www.afterschoool.tk
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In how many ways can we arrange STRANGE so that vowels occupy only odd places?
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We have 7 letters in this word. We have only 2 vowels, but we have 4 odd places and 3 even places. We have to use 4p2 to find all possibilities for vowels – thus we have 4! / 2! Or we have 4*3*2*1 / 2*1 = 12 possibilities We have now 5 places left out , for these, we have 5 consonants. Thus we have 5p5 options, or 5! Or 120 options. Thus we have 120 * 12 = 1440 options for arranging STRANGE.
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8 points are marked on the circumference of a circle. The number of chords obtained by joining these points in pairs is ?
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In order to make a chord, we need 2 points. We have to obtain any 2 points out of these 8 points. Here order doesn’t matter, we have to only select any 2 points, so we shall use the formula of combination (selecting) 8C2 or 8! / (2! * 6!) = 8*7 / 2*1 = 28 answer.

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A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y. is a member. The number of committee is ?
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Let us first form a committee with 3 ladies and 4 gents. We have 7C4*8C3 (it is selection only, so apply the formulae of combination). We get: 1960 Let us now calculate the possibility when Mrs.X and Mr. Y are together. We have 6c3*7c2 = 420 Let us deduct 1960-420 = 1540 ans.
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Solution . . .
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7C4*8C3 =7C4= 7*6*5 / 3*2*1 = 35 8C3 = 8*7*6/3*2*1 = 56 We get 56*35 = 1960 6c3*7c2 = 6c3 = 6*5*4/3*2*1 = 20 7c2= 7*6/2*1 = 21 We get 20 * 21 = 420
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The high court has given a 6 to 3 decision in favour of a matter. In how many ways can it give a decision against the matter?
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There are 9 judges. They can give decision in the following manner: All 9 against, 2. 8 against , 3. 7 against , 4. 6 against and , 5. 5 against and 4 in favour. Let us add all these possibilitites. 9C9, 2. 9c8, 3.9c7, 4.9c6, 5.9c5 = 1+9+36+84+126 = 256 answer.
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Solution . . .
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9C9 = 9! / (9! * 0!) = 1 9C8 = 9! / ((9-8)! *8!) =9!/8! = 9 9c7 =9*8/2*1 = 36 9C6 = 9!/ ((9-6)!*6!) = 9!/(3! * 6!) =9*8*7 / 3*2*1 = 84 9C5= 9!/ ((9-5)!*5!) = 9!/(4!*5!) =9*8*7*6/4*3*2*1 = 126
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I have to attempt 6 questions from my paper containing 12 questions divided in two equal sections. From one section I can take maximum 4 question. How many options do I have?

I have 3 possibiliities : 4 from section 1, 2 from section 2. or 3 from section 1 and 3 from section 2 OR 2 from section 1 and 4 from section 2. 6c4*6c2 + 6c3*6c3 + 6c2*6c4 =225+400+225 = 850 answer.
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How many factors does 75600 has ?
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Let us write down all the factors of 75600. we get 2*2*2*2*3*3*3*5*5*7 =thus we have 2^4 * 3^3* 5^2 *7^1 Thus we get 4 factors of 2, 3 factors of 3, 2 factors of 5, and one factor of 7. Formulae = (N+1)(N+1) . . . -1 N = number of factors of a factor = for example 2 is coming four times, is N for 2 is 4. (4+1)(3+1)(2+1)(1+1) - 1 =(5*4*3*2) – 1 =120-1 = 119 answer.

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How many 4 digit numbers can be formed from digits 1,1,2,2,3,4?
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We have six digits and there are two repeatition (1,2). Here order is important, so we shall use permutation (not combination), because 1122 is different from 2211. We have 6P4 divided by 2! *2! Thus we get 360 / 4 = 90 answer.
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In how many was can we divide 9 things among 3 groups containing 2,3,4 items?
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9C2 * 7C3 * 4C4 * =36*35*1 =1260 answer.

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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.

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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?
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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
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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:
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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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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 material FOR PGPSE PARTICIPANTS
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Components
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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
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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
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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
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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
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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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