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% (01:04) correct 33% (01:21) wrong based on 810 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

1

This post received KUDOS

2

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.
_________________

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