Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Nov 2011
Posts: 8

If a code word is defined to be a sequence of different [#permalink]
Show Tags
28 Jan 2012, 03:59
19
This post was BOOKMARKED
Question Stats:
67% (02:05) correct
33% (01:23) wrong based on 694 sessions
HideShow timer Statistics
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words? A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 28 Jan 2012, 04:02, edited 1 time in total.
Added the OA



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: Ratio [#permalink]
Show Tags
28 Jan 2012, 04:02
5
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is \(P^5_{10}\); # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is \(P^4_{10}\); \(Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}\). Answer: E.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 24 Mar 2010
Posts: 80

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
23 Dec 2012, 13:29
4
This post received KUDOS
1
This post was BOOKMARKED
Numbers of Options applicable for 5 letter digit > \(10 * 9 * 8 * 7 * 6\) ( as option pool for first digit is 10, for second 9 because one is removed and so on) Numbers of Options applicable for 5 letter digit > \(10 * 9 * 8 * 7\) Required Ratio > \((10 * 9 *8 * 7 * 6)/(10 * 9* 8 * 7)\) = \(6:1\)
_________________
 Stay Hungry, stay Foolish 



Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
28 Dec 2012, 06:43
2
This post received KUDOS
1
This post was BOOKMARKED
RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Number of 5letter code formed from 10 letters: \(=10*9*8*7*6\) Number of 4letter code formed from 10 letters: \(=10*9*8*7\) Answer: 6 to 1 or E
_________________
Impossible is nothing to God.



Director
Joined: 28 Jul 2011
Posts: 539
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)

Re: Ratio [#permalink]
Show Tags
30 Mar 2013, 09:04
Bunuel wrote: RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is \(P^5_{10}\); # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is \(P^4_{10}\); \(Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}\). Answer: E. Hi Bunnel, In this problem you have used Permutations, but in the problem you have used combination, which also deals with code aresearcherplanstoidentifyeachparticipantinacertain134584.htmlCan you please when to use permutaions or Combinations in these type of problems?
_________________
+1 Kudos If found helpful..



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: Ratio [#permalink]
Show Tags
31 Mar 2013, 08:51
mydreammba wrote: Bunuel wrote: RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is \(P^5_{10}\); # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is \(P^4_{10}\); \(Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}\). Answer: E. Hi Bunnel, In this problem you have used Permutations, but in the problem you have used combination, which also deals with code aresearcherplanstoidentifyeachparticipantinacertain134584.htmlCan you please when to use permutaions or Combinations in these type of problems? In this case the order of the letters matters, but in other question we are only interested in codes which are in alphabetical order (so we are interested in only one particular order). This post might help: aresearcherplanstoidentifyeachparticipantinacertain134584.html#p1150091
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15916

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
16 Apr 2014, 22:24
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Senior Manager
Joined: 15 Aug 2013
Posts: 311

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
23 Aug 2014, 10:51
Bunuel wrote: RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is \(P^5_{10}\); # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is \(P^4_{10}\); \(Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}\). Answer: E. Hi Bunuel, A couple of clarifications as i'm going through similar problems: 1) In this case, we use permutations because order DOES NOT matter. Correct? 2) If the problem said that we had to use the letter in alphabetical order, then order would matter and we would have to use the Combination formula over permutation. Correct? 3) Permutation and Combination both assumes that the letters/numbers CANNOT be repeated. Correct?



LBS Thread Master
Joined: 13 Jan 2015
Posts: 116
Location: United Kingdom
Concentration: Other, General Management

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 07:46
For the life of me,
My calculation does not give me the same answer.
The different part is the 10 Choose 4, my calculations are giving me different figures??
When i factorize top and bottom, i get 252/ 210??
Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 08:10



LBS Thread Master
Joined: 13 Jan 2015
Posts: 116
Location: United Kingdom
Concentration: Other, General Management

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 08:18
Hello Bunuel,
Thank you very much for responding.
My problem with your initial calculation is that when i do understand how you got 6! in the bottom part of your example above.
When i calculate it, it goes 10 Choose 5 is = 10*9*8*7*6 / 5*4*3*2*1
And then 10 Choose 4 i= 10*9*8*7 / 4*3*2*1
when I calculate 10 Choose 5 / 10 Choose 4.... I get 6/5
I do not know where the error is coming from
Thanks alot



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 08:23



LBS Thread Master
Joined: 13 Jan 2015
Posts: 116
Location: United Kingdom
Concentration: Other, General Management

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 08:30
Once again, thanks for your response,
sorry about the notations
My main issue is with the 10 Choose 4 (Denominator) , my understanding is that in order to perform this calculation, I take the first 4 terms of 10! starting with 10 and divide that by 4 factorial.
I do not understand how you get 6! here
Thanks once again and i am very grateful for your time here



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 08:32



LBS Thread Master
Joined: 13 Jan 2015
Posts: 116
Location: United Kingdom
Concentration: Other, General Management

If a code word is defined to be a sequence of different [#permalink]
Show Tags
31 Jan 2015, 08:33
I am so so sorry, I was doing a Combination instead of a Permutation Thank you very much



Manager
Joined: 23 Jan 2013
Posts: 172
Concentration: Technology, Other
GMAT Date: 01142015
WE: Information Technology (Computer Software)

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
07 Feb 2015, 11:31
In this case ABCDE is different from BCDEA hence order matters boils down to using permutations ...
Hence ( 10! / 5 ! ) * ( 6! / 10 ! ) = 6/1 Answer is E



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15916

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
14 Mar 2016, 02:41
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Director
Joined: 17 Dec 2012
Posts: 550
Location: India

If a code word is defined to be a sequence of different [#permalink]
Show Tags
18 Mar 2016, 02:42
Take 1 case: ABCDE for 5 letter code and ABCD for 4 letter code. You Choose 5 at a time and 4 at a time and order is important. So the formula is nPr. Therefore the ratio is 10P5/ 10P4 = 6:1 Hence E.
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com
Classroom and Online Coaching



Intern
Joined: 30 Dec 2015
Posts: 5

Re: If a code word is defined to be a sequence of different [#permalink]
Show Tags
04 Nov 2016, 02:52
Hi, i am confused why we dont care about the order of selection of 5 characters first then 4 characters or 4 characters first then 5 characters. My work is as below, can someone point out where did i do wrong?
First selection: Ways of 5 characters to be selected in the beginning: 10 x 9 x 8 x 7 x 6 = 30240 Ways of 4 characters to be selected then: 5 x 4 x 3 x 2 =120
Second selection: Ways of 4 characters to be selected first: 10 x 9 x 8 x 7 = 6860 Ways of 5 characters to be selected then: 6 x 5 x 4 x 3 x 2 = 720
So total of ways for 5 characters: 30960 total of ways for 4 characters: 6980
Ratio 5 characters: 4 characters = 4.436??




Re: If a code word is defined to be a sequence of different
[#permalink]
04 Nov 2016, 02:52







