Exercise :: Permutation and Combination - General Questions Show
Page 2
Exercise :: Permutation and Combination - General Questions
Jamboree GMAT Instructor Joined: 15 Jul 2015 Status:GMAT Expert Affiliations: Jamboree Education Pvt Ltd Posts: 257 Location: India
How many 5 letter words ( with or without meaning) can be formed using [#permalink]
00:00
Difficulty:
Question Stats: Hide Show timer StatisticsHow many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and T so that letter P is to the left of letter R?(A) 120(B) 60(C) 48(D) 24 (E) 12 _________________
Aryama Dutta Saikia
Formatted the question
Verbal Forum Moderator Joined: 08 Dec 2013 Status:Greatness begins beyond your comfort zone Posts: 2218 Location: India Concentration: General Management, Strategy GPA: 3.2 WE:Information Technology (Consulting)
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink] It seems there are only 4 distinct letters in the question stem .
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
SVP Joined: 20 Mar 2014 Posts: 2436 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE:Engineering (Aerospace and Defense)
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink]
AryamaDuttaSaikia wrote: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and T so that letter P is to the left of letter R?(A) 120(B) 60(C) 48(D) 24 (E) 12 We can solve this qustion by 2 methods,Method 1: Total combinations for 5 letters = 5! = 120 As there is no bias in counting the combinations, half of the combinations will have R to the left of P and half of them to the right of P.Thus possible combinations = 120/2 = 60. B is the correct answer.Method 2: The combinations possible are:PRQST, combinations of RQST = 4! =24QPRST, combinations = 3C1*3!, 3C1 taken to account for the fact that instead of Q we can also take S or TQSPRT, combinations = 2!*2!*3C2, 3C2 taken to account for the fact that instead of QS we can also take ST or QT, 2! each to take into account permutations for QS and RTQSTPR, combinations = 3!*1, 3! to account for permutations for QSTThus, the total combinations possible = 4!+3C1*3!+2!*2!*3C2+3! = 24+18+12+6=60. B is the correct answer. _________________
GMAT Club Legend Joined: 08 Jul 2010 Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator Posts: 5884 Location: India GMAT: QUANT EXPERT Schools: IIM (A) WE:Education (Education)
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink]
AryamaDuttaSaikia wrote: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and T so that letter P is to the left of letter R?(A) 120(B) 60(C) 48(D) 24 (E) 12 Best Method: Total Ways of arranging 5 letters in any possible order = 5*4*3*2*1 = 5! = 120in Half of the cases P will be to the left of R and in other half P will be to the right of RHence, Desired outcome = 120/2 = 60Alternate method: we have five blank spaces _ _ _ _ _ which have to occupied by these 5 letter such that P is to the left of Rso let's select two blank spaces for P and R out of 5 blank spaces, No. of ways of selecting two blank spaces out of 5 = 5C2 = 10The no. of ways of arranging P and R on selected two places such that P is to the left of R = 1No. of ways of arranging remaining three letters on remaining three blank spaces = 3*2*1 = 3! = 6Total Ways of Arrangement = 5C2 * 1 * 3! = 10 * 1 * 6 = 60Answer: option B _________________
GMATinsight SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l GMAT730+ESCP FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. l NEW:QUANT REVISION Topicwise Quiz
Jamboree GMAT Instructor Joined: 15 Jul 2015 Status:GMAT Expert Affiliations: Jamboree Education Pvt Ltd Posts: 257 Location: India
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink] Conceptual wayAs a general strategy in basic Question on Permutation Combination like this we first arrange the letters on which there is a condition and then arrange the remaining letters. So out of the five positions where the 5 letters needs to be arranged we will first arrange letters P and R. So letters P and R will take two positions so lets select two positions out of 5 positions where letters P and R will be placed Two positions can be selected out of 5 positions in 5C2 ways = 10 ways. Once two positions have been selected we know P will be in the left position and R will be in right so there is only one way we can place letters P and R in these two positions. And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways. So the final Answer = number of ways letters P and R can be arranged x number of ways the other 3 letters can be arranged Final Answer = 10 x 6 = 60 ways JAMBOREE Way Now 5 letters can be placed in 5 positions in 5! Ways = 120. Logically we can analyze that either letter P will be to the left of letter R or to the right of letter R. So by simple reasoning we will get that in half of the ways letter P will be to the left of letter R.So the correct answer = ½ total number of ways = 60 waysWe make the GMAT simple! _________________
Aryama Dutta Saikia
Intern Joined: 27 Jun 2015 Posts: 12
How many 5 letter words ( with or without meaning) can be formed using [#permalink] Why can't I consider PR as one letter? So I only have 4 letters which can be rearranged.(PR) Q S T n = 4! = 24? Where is my mistake? I don't understand it Thank you very much.
Verbal Forum Moderator Joined: 08 Dec 2013 Status:Greatness begins beyond your comfort zone Posts: 2218 Location: India Concentration: General Management, Strategy GPA: 3.2 WE:Information Technology (Consulting)
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink]
22gmat wrote: Why can't I consider PR as one letter? So I only have 4 letters which can be rearranged.(PR) Q S T n = 4! = 24? Where is my mistake? I don't understand it Thank you very much.You have only considered the case in which R is to the immediate right of P , but as per the question stem R can take any of the positions to right of P ( other letters can come in between)P _ _ _ _R can take any of the 4 positions as long as it satisfies being to right of P.PRQST , Combination of RQST =4!=24whereas as per your procedure , (PR) Q S T , there will be 3! combinations for this configuration.And you can proceed similarly for the other configurations .QPRST-3C1*3!QSPRT- 2!*2!*3C2QSTPR- 3!*1 Hope it helped !!
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
GMAT Expert Joined: 16 Oct 2010 Posts: 13132 Location: Pune, India
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink]
22gmat wrote: Why can't I consider PR as one letter? So I only have 4 letters which can be rearranged.(PR) Q S T n = 4! = 24? Where is my mistake? I don't understand it Thank you very much. You might find this post useful: http://www.veritasprep.com/blog/2011/10 ... s-part-ii/ _________________
KarishmaOwner of Angles and Arguments at https://anglesandarguments.com/ NOW PUBLISHED - DATA SUFFICIENCY MODULE For Individual GMAT Study Modules, check Study Modules > For Private Tutoring, check Private Tutoring >
Intern Joined: 27 Jun 2015 Posts: 12
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink] Thank you all!
Non-Human User Joined: 09 Sep 2013 Posts: 24231
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: How many 5 letter words ( with or without meaning) can be formed using [#permalink] 28 Jun 2021, 02:42 |