30 july business mathematics

8/14/2019 30 July Business Mathematics

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www.afterschoool.tk AFTERSCHOOOL MATERIAL FO

BUSINESS MATHEMATICS

AFTERSCHOOOL DEVELOPING CHANGEMAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP

PGPSE PROGRAMME

World Most Comprehensive programme in socialentrepreneurship & 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
http://www.afterschool.tk/http://www.afterschoool.tk/http://www.afterschoool.tk/http://www.afterschool.tk/


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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.


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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 redballs?

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 select so that we have one ofeach colour?

Now we have 7c1 * 6c1 * 4c1.

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


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we select so that we dont have anyred 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.


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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 wecan 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? Tarachandwants to give presentation before

Hulash?

We have 4 speakers. They can be arranged

in 4! Or 24 ways. But in some of the casesTarachand will be behind Hulash, we haveto remove those cases. Let us keepTarachand just behind Hulash and rotateothers, we have 3! = 6 cases. Let us

consider Tarachand with a gap of 1 place.We have 2 cases. We have one case whenthere is a gap of 2 between Tarachand andHulash. Thus we have 24-9 = 15 cases.Answer.


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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 speakingbefore A. There are many such cases. Let us take

BA as one combination. We have 24 ways withBA. Let us take B-A (one gap), we have differentcombinations like B-A- - or b-a- or - - b-a, thuswe have 18 such options. We can have 2 gapsbetween B & A. which can be B - - A- or B - - A.

thus we have 12 such options. We can have 3gaps between B & A and there are 6 suchoptions. Thus answer is 120 (24+18+12+6) = 60answer.


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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 becollinear. Thus we have to remove allsuch cases where points are collinear.

12c 3 5c312*11*10/3*2*1 5*4/2*1=220 10=210 answer.


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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 c216! / (14! * 2!)

16*15 / 2*1

=8*15

=120 answer.


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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! = 5040R = 7 answer.


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THERE ARE 5 CANDIDATES AND 3

MEMBERS TO BE ELECTED. IN HOW

MANY WAYS CAN A VOTER VOTE?

The voter has a choice, he may give 1 vote,2 vote or 3 votes. He has 5 choices in eachcase.

If he gives one vote, his choice is 5c1, if hegives 2 votes, his choices are 5c2, if hegives 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, so12c4 is the combination.

Thus we have to select: (12c4 * 8c4 *

4c4)/ 3!Thus we have 5775 answer


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ABOUT A FTERSCH OOOLAfterschoool 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 forCS / CFP / CFA /CMA / FRM. This

course is also available online also. It also conductsworkshops 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?

To promote people to take up entrepreneurship

and help develop the society

To enable people to take up franchising andother 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

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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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 weekendclasses

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 studymaterial


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Components

Pedagogy curriculum and approach based on IIM Ahmedabad and ISBHyderabad (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 itsbranches in important cities in Indiaincluding Delhi, Kota, Mumbai, Gurgaonand other important cities.Afterschooolians will be responsible formanaging and developing these

branches and for promoting socialentrepreneurs.


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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 yourselfonly
http://www.afterschoool.tk/


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www.afterschoool.tk

social entrepreneurship for better

society
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30 july business mathematics

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