Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
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
00:00
A
B
C
D
E
Difficulty:
35% (medium)
Question Stats:
67% (02:06) correct
33% (01:25) wrong based on 667 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 5-letter code words to the number of 4-letter code words?
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 5-letter code words to the number of 4-letter 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 \(P^4_{10}\);
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 -> \(10 * 9 * 8 * 7\)
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 5-letter code words to the number of 4-letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1
Number of 5-letter code formed from 10 letters: \(=10*9*8*7*6\) Number of 4-letter code formed from 10 letters: \(=10*9*8*7\)
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 5-letter code words to the number of 4-letter 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 \(P^4_{10}\);
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 5-letter code words to the number of 4-letter 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 \(P^4_{10}\);
Can 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).
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.
_________________
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 5-letter code words to the number of 4-letter 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 \(P^4_{10}\);
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?
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
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
Please follow the link given in my previous post.
_________________
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.
_________________
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.
_________________
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??
gmatclubot
Re: If a code word is defined to be a sequence of different
[#permalink]
04 Nov 2016, 02:52
There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...
This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...
Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...
close
67% (02:06) correct
9
