22 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

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WHAT IS THE DIFFERENCE BETWEEN PERMUTATION & COMBINATION? 

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In permutation, order is important. In combination, only selection is important – order is not important. Suppose you have to select 3 of your friends for party = combination will apply – as it hardly matters as to who is no. 1 or no. 2 or no.3 If you are asked to form numbers from 1,2,3 permutation will apply, as 123 is different from 321.

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How many 4 digit numbers can you form from 1,3,4,5 – using each digit only once?  This

is example of permutation.  Solution: 4 p 4  It is written as 4! Divided by (4-4)!  4! = 4*3*2*1  4*3*2*1 / (4-4)!  0! = 1.  Thus answer is 24 answer. www.afterschoool.tk

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There are 12 patients waiting for a doctor. Doctor can see only 1 patient at a time. In how many ways can he schedule his patients?  12

p 12  12! Divided by(12-12)!  12*11*10*9*8*7*6*5*4*3*2*1 divided by 1  =479001600 answer.

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You have to select one Prime minister and 1 Dy. Prime minister out of 10 MPs. One person can hold one post. All MPs want to be PM. How many options do you have?  10

P2  10*9*8*7*6*5*4*3*2*1 divided by 8*7*6*5*4*3*2*1  =10*9  =90 answer. www.afterschoool.tk

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12 schools are participating in a quiz contest. In how many ways can 1st ,2nd 3rd prize be won by them?  12

p3  =12*11*10  =1320 answer.

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How many words can you make using all the letters from COMPUTER?  COMPUTER

has 8 letters.  Thus 8p8 gives you 8!  8! = 40320 answer.

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In how many ways can you rearrange the word FAILURE that new words are formed with all the letters, however, vowels are always together? 

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There are 4 vowels. We treat them as one. Now we have FLR as other letters. We have 4 letters in all (FLR and Vowels). They can be arranged in 4! (4P4) ways = 24. 4 vowels can be arranged among themselves in 4! Ways so they can be arranged in 24 ways. Total ways are 24*24 = 576 answer.

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In how many ways can you frame new words from all the letters of DAUGHTER, where vowels occupy odd positions? 

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There are 3 vowels. And 4 odd positions. So we have to use one consonant also for these 4 positions. Thus we have 4 letters for 4 odd positions which give us 4! = 24. Now we have 4 even position left. Thus we have 4! Options. The total number of options are 24*24 = 576 answer. Alternatively, 3! * (5!-4!) = 6*96 = 576 answer.

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In how many ways can we arrange the word TRIANGLE so that ANGLE is always present?  There

are 4 letters for us: 1. T, 2, R, 3, I, 4, angle.  Thus we have 4! = 24 answer.  (we have taken angle as single letter).

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What is the sum of all letters that can be formed from 1,2,3?    

Total number of letters that can be formed is 3! = 3*2*1 = 6. 6/3 = 2 every letter comes twice Every letter will occupy a position 2 times. (thus 3+2+1 = 6 *2 = 12. Each position will have 12 as total. 12 for last, 12 for 10th and 12 for 100th position. Shortcut = We can multiply 12 with 111 to get the answer: 1332 answer.

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Find the total of all the numbers that we can form from 2,4,6,8?  (2+4+6+8)

= 20.

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= 24  24 / 4 = 6, so each letter will come 6 times.  Thus 20*6*1111=133320

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Find the sum of all the letters that can be formed from 12345?  There

are 5 digits, the total is: (1+2+3+4+5) = 15  Total number of options 5! = 120  120 / 5 = 24  = 15*24*11111  =3999960 answer

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What is the total of all the numbers that can be formed from 1,2,3,4,5,6, using each digit once only?  Total

of all the digits is 21.  Total options 6! = 720.  Each digit comes at a place 720/6 = 120 times.  Thus total is 21*120*111111  =279999720 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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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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