Quant Study Notes: Permutation and Combinations

Dear Readers,
Today we’ll discuss about Permutation and Combination. This topic is can fetch you marks easily but you need to know the right concepts and types of questions to practice.

ALL ABOUT PERMUTATION AND COMBINATION PERMUTATION

Permutations are different numbers of arrangements. Making words of 4 letters without repetition or with repetition is an example of permutation. Now suppose we have to make a word of 4 letters by taking any 4 letters from 10 letters A, B, C, D, E, F, G, H, I

☞ For example, permutations of 4 distinct objects out of  20 distinct objects can be written as 

COMBINATION

A combination is a grouping or selection of all or part of a number of things without reference to arrangement of the things selected.

For example selection of three members from a family of ten, number of cricket matches in a group having 10 teams, number of triangles formed by joining any three points out of 20 points in plane etc.

☞ The symbol

 represents total number of selections taking r different objects out of n different objects.

Suppose there are 5 students and a company wants to select any 3 of them. So the total number of ways = selection of 3 out of 5 = rejection of 2 out of 5.

WORD FORMATION

Word formation is based on fundamental principle of multiplication. 

☞ For example, total number of words which can be formed by using the letters of the word “ACHILLES” will be 8!/2!, as the letter L appeared twice.

GAP METHOD

Gap method is used if we have to arrange ‘n’ different things in such a way such that no two of the ‘r’ things are together. In this method we first place (n – r) things in a line so that there are (n – r + 1) gaps in between and at extreme ends. Now place ‘r’ things on these gaps so that no two of these things are together provided that r ≤ n – r + 1. Suppose T1,T2,T3,………… T10 are 10 distinct objects and we want that no two of T1,T2,T3 and T4 are together in the arrangement. First place remaining things T5,T6……… T10

_T5_T6_T7_T8_T9_T10_

So there are 7 gaps

Total number of ways = (7.6.5.4).6!

RANK OF A WORD IN DICTIONARY

If all the words which can be made by using n different letters are arranged in a dictionary in alphabetical order then position at which a particular word appears, is known as its rank. For example 24 words can be made by using letters of the word “RANK” without repetition. Now to calculate position of the word “RANK” we arrange the words in alphabetical order.

Hence position of the word RANK is:

3! + 3! + 3! + 1 + 1 = 20

SUM OF ALL THE NUMBERS WHICH CAN BE FORMED BY USING THE DIGITS WITHOUT REPETITION

Suppose the digits are 1, 2, 3, 4. We know that total number of numbers which can be formed without repetition is 4! = 24. Now

Numbers with unit digit 1 will be 3! = 6

Numbers with unit digit 2 will be 3! = 6

Numbers with unit digit 3 will be 3! = 6

Numbers with unit digit 4 will be 3! = 6

Hence sum of the unit digits

= 6 × (1 + 2 + 3 + 4) = 60,

Similarly sum of the digits at tens, hundred’s and thousand’s place = 60

Sum of all the numbers

= 60 × 1 + 60 × 10 + 60 × 100 + 60 × 1000 = 66660

Sum of all the numbers which can be formed by using the ‘n’ non zero digits without repetition is (n – 1)! (sum of the digits) (111……n times).

CIRCULAR PERMUTATION

☞Number of circular permutations of n distinct objects = (n – 1)!

☞Number of circular permutations of n distinct objects =

if there is no difference between clock wise and anticlockwise permutations.

Cloze Test and Double Fillers

P

Directions (Q.1 – Q.10): In the following passage, some of the words have been left out, each of which is indicated by a number. Find the suitable word from the options given against each 
number and fill up the blanks with appropriate words to make the paragraph meaningfully complete. 
The idea to monetise gold is by no (1) new. In fact, various schemes to (2) the gold (3) already exist. Though launched with a lot of fanfare, they have (4) very little subscription. On economic as well as practical grounds, there has been a continuing need for a scheme, which would basically seek to (5) gold now lying idle in households, religious institutions and so on and convert them into financial assets. The objective has been to remove the disincentives that have (6) earlier schemes. The bait offered is interest plus the promise that those who deposit gold now can take it back as gold. The interest rate offered on similar schemes so far has been nominal, and this might have been a (7) to many prospective depositors. In the latest scheme, there is a promise of tax exemption on top of higher interest rates. If implemented, that would enhance the attractiveness of the scheme but — for many other reasons — will hardly be a clincher. Even more problematic is the sales pitch based on ‘gold in gold out’, meaning you can take back your initial investment in the same form, namely as gold. This is (8) even though the government is not (9) facts. However, much the government assures them that the gold value will be protected and that even the interest will be paid in gold, there is bound to be a (10) from many households. This is because gold in the jewellery will be melted down after removing the sludge in the form of bars.

Q1. 

1) respect
2) distress
3) fact
4) means
5) season

Q2. 

1) account
2) recurring
3) tap
4) pious
5) bid

Q3. 

1) hoard
2) tried
3) link
4) aura
5) crux

Q4. 

1) dispersed 

2) garnered
3) used
4) attached
5) threw

Q5. 

1) disgust 

2) lure
3) prevent
4) shun
5) release

Q6. 

1) squandered 

2) dissipated
3) debt
4) agglomerate
5) bedevilled

Q7. 

1) deterrent 

2) preserved
3) promoted
4) above-board
5) encouragement

Q8. 

1) catalyst 

2) reliable
3) deceptive
4) incentive
5) upright

Q9. 

1) liking 

2) secret
3) computing
4) distorting
5) denounced

Q10. 

1) submission 

2) resistance
3) choice
4) compliance
5) conforming

Directions (Q.11–Q.15): In each of the following sentences there are two blank spaces. Below each sentence there are five pairs of words denoted by the numbers 1 , 2 , 3 , 4 and 5 . Find out which pair of words can be filled up in the blanks in the sentence in the same sequence to make it meaningfully complete. 
11.There are several ways in _________ government as well ordinary citizens can ______________ literacy. 

1) that, prove 

2) that, advance
3) which, spread
4) which, suppress
5) it, disseminate

12.Such a _________ , ____________ in food grain production means a heavy loss for farmers. 

1) drastic, drop 

2) extreme, slop
3) mild, lead
4) exorbitant, steep
5) collected, crisis

13.There are only a few companies who can __________ projects of this __________. 

1) adjust, level 

2) handle, magnitude
3) manage, height
4) cooperate, box
5) arrange, depth

14.The solutions are to avoid the _________ altogether, by ___________ a slightly different route. 

1) impasse, taking 

2) clitches, using
3) plights, showing
4) gridlock, liking
5) dilemma, tracking

15.The number of students _______ sick has reduced ____________ because of the new sports facilities. 

1) having, almost 

2) claiming, more
3) being, little
4) complaining, highly
5) reporting, significantly

Answer Key –

Answer 1. 4
Answer 2. 3
Answer 3. 1
Answer 4. 2
Answer 5. 2
Answer 6. 5
Answer 7. 1
Answer 8. 3
Answer 9. 4
Answer 10. 2
Answer 11. 3
Answer 12. 1
Answer 13. 2
Answer 14. 1
Answer 15. 5

Nobel Prize 2016 Winners List - At A Glance

Dear Readers,

Today we are presenting you a short note on winners of Nobel Prize 2016. On 27 November 1895, Alfred Nobel signed his last will and testament, giving the largest

share of his fortune to a series of prizes in Physics, Chemistry, Physiology or Medicine, Literature and Peace - the Nobel Prizes. In 1968, Sveriges Riksbank (Sweden's central bank) established The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. Here we are representing you the winners list of Nobel Prize 2016.

Nobel Prize 2016 Winners List - At A Glance

Category	Edition	Winner(s)	Work/Contribution	Remarks
Physiology & Medicine	107th	Yoshinori Ohsumi (Japan)	for his discoveries of mechanisms for autophagy.
Physics	110th	David J. Thouless (UK) F. Duncan M. Haldane (US) J. Michael Kosterlitz (UK)	for their theoretical discoveries of topological phase transitions and topological phases of matter.	The Nobel Prize in Physics 2016 was divided, one half awarded to David J. Thouless, the other half jointly to F. Duncan M. Haldane and J. Michael Kosterlitz.
Chemistry	108th	Jean-Pierre Sauvage (France) Sir J. Fraser Stoddart (UK) Bernard L. Feringa (Netherlands)	for the design and synthesis of molecular machines.
Peace	97th	Juan Manuel Santos (President of Colombia)	for his resolute efforts to bring the country's more than 50-year-long civil war to an end, a war that has cost the lives of at least 220000 Colombians and displaced close to six million people.	Juan Manuel Santos has decided to donate the money from the Nobel Prize to the conflict victims in Colombia.
Economic Science	48th	Oliver Hart (UK) Bengt Holmstrom (Finland)	for their contributions to contract theory, shedding light on how contracts help people deal with conflicting interests.
Literature	109th	Bob Dylan (USA)	for having created new poetic expressions within the great American song tradition

Thanks.

Daily GK Update: 13th October, 2016

International Day for Disaster Reduction: October 13

i. International Day for Disaster Reduction is observed annually on 13 October. 

ii. This year theme is Live to Tell: Raising Awareness, Reducing Mortality.



Bob Dylan wins 2016 Nobel prize in literature
i. American singer-songwriter Bob Dylan has been awarded the Nobel Prize in Literature 2016 "for having created new poetic expressions within the great American song tradition". 
ii. Dylan, 75, has won numerous awards, including twelve Grammys and one Academy Award.

Bank of Baroda signs brand endorsement with Sindhu, Srikanth

i. Public lender Bank of Baroda today sealed a principal sponsorship contract with badminton Olympians P V Sindhu and K Srikanth.

ii. The three-year deal with the two players was agreed in-principle before they represented and made India proud on the international stage at the Rio 2016 Olympics.

Bank of Maharashtra renews tie-up with United India Insurance

i. State-run Bank of Maharashtra has renewed its corporate agency tie-up with United India Insurance Company. 

ii. Customers can buy the entire gamut of UIIC products at any of the 1,896 branches of the bank across the country.

Ramesh Pokhriyal Nishank awarded by Ugandan govt for his literary work

i. Former Uttarakhand chief minister Ramesh Pokhriyal Nishank has been conferred with a prestigious award by the Ugandan government for promoting human values through his literature.

India donates Rs. 9.3 million to Mandela Foundation

i. India donated Rs. 9.3 million to the Nelson Mandela Foundation to help it in its welfare work for the people of South Africa. 

ii. The Nelson Mandela Foundation was established in 1999 after the then President Nelson Mandela stepped down as the President of South Africa.

Govt appoints G Mahalingam as Sebi whole-time member

i. The government has appointed Reserve Bank's Executive Director G Mahalingam as a Whole-Time Member of markets regulator Sebi.

ii. Apart from the Chairman, the Securities and Exchange Board of India (Sebi) can have three Whole-Time Members (WTMs).

ICICI Bank first Indian lender to execute Blockchain transaction

i. ICICI Bank has become the first Indian lender to complete a banking transaction using Blockchain technology.

ii. This remittance transaction has been completed in partnership with Emirates NBD, a lender from the West Asia

Coordinated Patrol and India-Indonesia Bilateral Maritime Exercise commence in Indonesia

i. The 28th India and Indonesia Coordinated Patrol (CORPAT) and Second Bilateral Maritime Exercise have commenced at Belawan, Indonesia in the Andaman Sea.

Cabinet approves setting up of IIM Jammu

i. The Cabinet today approved the setting up of an Indian Institute of Management in Jammu as part of PM Narendra Modi's development package for Jammu and Kashmir. 

ii. The government recently set up an Indian Institute of Technology in Jammu. 

Punjab Agricultural University signs MoU with FieldFresh to promote crop research

i. Punjab Agricultural University and FieldFresh Foods, a joint venture between Bharti Enterprises & Del Monte Pacific Limited have signed a Memorandum of Understanding (MoU) to carry out a corn productivity research programme.

ii. The MoU follows the agreement signed recently between Cambridge University and Bharti Foundation to fund the research Programme.

Cabinet approves pact between EXIM Bank, NDB

i. Union Cabinet today approved a pact between Export-Import Bank of India and BRICS-promoted New Development Bank, along with other development financial institutions of member nations, with an aim to strengthen trade and economic ties.

ii. The New Development Bank (NDB) aims to mobilize resources for development projects in BRICS, emerging economies and developing countries