23 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

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

I HAVE 6 FRINEDS, IN HOW MANY WAYS CAN IN INVITE THEM FOR DINNER? 

   

I may invite 1, 2, 3,4,5, or all 6. I may invite any combination out of these. But I have to invite at least one of them. FORMULAE = 2 ^n -1 =2^6 -1 =64-1 = 63 Note : here if it is not necessary to invite at least one person, then the answer will be 64.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

THERE ARE 4 BOYS AND 3 GIRLS IN DEBATE GROUP. ONE COMMITTEE IS TO BE FORMED WITH AT LEAST 2 GIRLS. COMMITTEE WILL CONSIST OF 4 MEMBERS. HOW MANY OPTIONS DO WE HAVE? 

    

We can take 4 members as 2 boys and 2 girls or 3girls and 1 boys (total has to be 4 members only). We can select 2 boys and 2 girls. 4c2 * 3c2 = 6*3 = 18 We can select 1 boy and 3 girls 4c1 * 3c3 = 4*1 = 4 No. of options = 18+4 =22 answer

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Continued .. .. Answer .. 4c2 * 3c2 = 6*3 = 18  In this combination question, we take factorial of 4 (4*3*2*1) which is divided by 2*1 & (4-2)!, which is again 2*1. 

 4c2

= (4*3*2*1 )/ (2*1)(2*1) = 6  Similarly, 3c2 = 3! Divided by 2! & (3-2)!.  Which is (3*2*1)/(2*1)(1) = 3  =6*3 = 18. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

How many different words can be made from TARACHAND?  Here

we can see that we have 3 A.  The total number of letters is 9.  Answer: 9 ! / 3!  (take factorial of total number of letters, and divide it by the number of letters which are repeating).  =60480 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

I go for shopping with Rishabh. We have to purchase upto 4 electronics out of Friz,TV,Laptop, & AC. How many options do we have?  Formulae

= 2^n -1  =2^4 -1 = 15 answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

In a party there are 66 handshakes. Tell me how many persons were present, if each shook hand with each other?  If

there are 3 members, they will shake hands like this – 1st with 2, 2nd with 1 (one is already counted).  Thus when there are 6 members, the hand shakes are 5,4,3,2,1.  Similarly, when we have 12 members, we have 11+10+9+8+7+6+5+4+3+2+1 hand shakes. Answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

I have 2 books on Finance, 3 books on Management & 4 books on entrepreneurship. How can I put them on a shelf, books of a subject must be together?  There

are 3 subjects, so 3!.  Finance books can be exchanged among themselves, so 2!, similarly, for management books, 3!, similarly for entrepreneurship books 4!.  =3!*2!*3!*4! = 1728 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

How many ways can we rearrange word SUCCESS that the vowels are always together?  

   

There are 2 vowels – E & U Let us treat these as on letter. Now we have 6 letters. There are some repeatitions, which have to be divided. 6! / (2!*3!) =60 We can interchange vowels. Which give us 2 options. Thus 60 * 2 = 120 answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

In npr, how many factors are there?  Take

any hypothetical example.  Let us say 6p2,  Here we have factors as: 6*5*4*3  Thus we have n-r factors.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

10 examination papers are arranged in such a way that best and worst papers never come together. Number of arrangements is ?  Let

us count those arrangements, where best and worst come together. These arrangements are (10-1)!*2  Let us now count all arrangements of these 10 papers : 10!.  Thus our answer is 10! – (9! *2)Answer.  =2903040 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

The number of 4 digit numbers greater than 5000 can be formed out of the digit 3,4,5,6 and 7. Repeatition is not permitted. How many options do we have?  We

have 5 digits, out of which 3 can come in the first digit (5,6,7). Once we use this digit, we are left with (5-1) 4 digits.  For first digit we have 3 options, for next digit, we have 4 options, for next digit, we have 3 options and so on.  3*4*3*2* = 72 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Why such a programme? 







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

www.afterschoool.tk

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.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

www.afterschoool.tk

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)

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

www.afterschoool.tk social entrepreneurship for better society

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS