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:

A certain club has 20 members. What is the ratio of the memb [#permalink]

Show Tags

25 Mar 2009, 22:04

1

This post received KUDOS

8

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

73% (02:04) correct
27% (01:00) wrong based on 535 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?

A. 16 to 1 B. 15 to 1 C. 16 to 5 D. 15 to 6 E. 5 to 4

A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club? A. 16 to 1 B. 15 to 1 C. 16 to 5 D. 15 to 6 E. 5 to 4

20*19*18*17*16 does not give you # of 5 member committees out of 20. You need to divide this by 5! to get rid of the repetitions (factorial correction). The same for 20*19*18*17, you should divide this by 4!.

Take another example: how many committees of 2 can be formed out of A, B and C?

AB AC BC Only 3, which is \(C^2_3=3\).

But the way you are doing you'd get 3*2=6. This number has repetitions so we should divide it by 2! --> 6/2!=3.

Also, for this question, why can't we just do the following: (20*19*18*17*16)/(20*19*18*17) = 16/1?

20*19*18*17*16 is giving all possible ways of selecting 5 people. It also includes the order of a particular selection into account. In this case it does not mater if you select a member first ,second or third as long as it is selected in the group. Therefore, the 20*19*18*17*16 number has repetition of the same group in 5 ways and you have to divide by FACT[5]. Similarly for (20*19*18*17) by FACT[4]

20*19*18*17*16 does not give you # of 5 member committees out of 20. You need to divide this by 5! to get rid of the repetitions (factorial correction). The same for 20*19*18*17, you should divide this by 4!.

Take another example: how many committees of 2 can be formed out of A, B and C?

AB AC BC Only 3, which is \(C^2_3=3\).

But the way you are doing you'd get 3*2=6. This number has repetitions so we should divide it by 2! --> 6/2!=3.

Hope it's clear.

when should we use 20*19*18*17*16 way and when the second way?
_________________

20*19*18*17*16 does not give you # of 5 member committees out of 20. You need to divide this by 5! to get rid of the repetitions (factorial correction). The same for 20*19*18*17, you should divide this by 4!.

Take another example: how many committees of 2 can be formed out of A, B and C?

AB AC BC Only 3, which is \(C^2_3=3\).

But the way you are doing you'd get 3*2=6. This number has repetitions so we should divide it by 2! --> 6/2!=3.

Hope it's clear.

when should we use 20*19*18*17*16 way and when the second way?

The first case is applicable when the order matters, when, for example, we have member #1, member #2, ...
_________________

Re: A certain club has 20 members. What is the ratio of the memb [#permalink]

Show Tags

16 Feb 2015, 20:51

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: A certain club has 20 members. What is the ratio of the memb [#permalink]

Show Tags

03 May 2015, 20:29

dont remember the formular, gmat dose not test.

to take 5 20*19*18*17*16/5!

Princeton review book is very exccelent at explanation of combination and counting. no book can compete Princeton book in this section. read it to master combination and counting. this section is only a few pages and can be learn in a few hours.

this explanation in the book is concise, deep and comprehensive.

They didnt mentioned that first we have to select 5 members then 4 from the remaining 15?

That is exactly the reason why you need to treat "selecting 5 out of 20" and "selecting 4 out of 20" as 2 independent events. Per the question, there is no overlap in the 2 cases.

Thus the final answer = 20C5 / 20C4 = 16/5
_________________

They didnt mentioned that first we have to select 5 members then 4 from the remaining 15?

The question is absolutely clear and holds no ambiguity in the language

Question : A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?"

The two actions (making the committee of 5 members AND making the committee of 4 embers) are to be treated independently.

No. of Ways to make 5 member committee out of 20 members = 20C5 = 15504

No. of Ways to make 4 member committee out of 20 members = 20C4 = 4845

Required ratio = 15504 / 4845 = 16/5
_________________

Re: A certain club has 20 members. What is the ratio of the memb [#permalink]

Show Tags

27 Jul 2015, 05:22

Engr2012 wrote:

honchos wrote:

Isnt the Question doubtful?

They didnt mentioned that first we have to select 5 members then 4 from the remaining 15?

That is exactly the reason why you need to treat "selecting 5 out of 20" and "selecting 4 out of 20" as 2 independent events. Per the question, there is no overlap in the 2 cases.

Thus the final answer = 20C5 / 20C4 = 16/5

Thanks, My doubt is still the same. They didn't mentioned that two events are mutually independent or dependent. This is a very easy question, but I was spinned that how should I interpret the language - Mutually independent or independent.
_________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Dependent events is a very big information and will thus always be mentioned if that is the case. If not given, you have to treat the 2 events independently. You are over analyzing the question. The language is perfectly fine.
_________________

They didnt mentioned that first we have to select 5 members then 4 from the remaining 15?

That is exactly the reason why you need to treat "selecting 5 out of 20" and "selecting 4 out of 20" as 2 independent events. Per the question, there is no overlap in the 2 cases.

Thus the final answer = 20C5 / 20C4 = 16/5

Thanks, My doubt is still the same. They didn't mentioned that two events are mutually independent or dependent. This is a very easy question, but I was spinned that how should I interpret the language - Mutually independent or independent.

The question did NOT mentioned that "Team of 4 has to be selected out of the REMAINING"

If the word "remaining" has not been used then it is Independent event case.

Re: A certain club has 20 members. What is the ratio of the memb [#permalink]

Show Tags

09 Feb 2016, 13:33

Hello guys,

Can I please ask how 20C5 / 20C4 has been solved to get the fraction 16/5? I know that one way to solve this is by doing the long multiplication thing but Brunnel has calculated it in a simplified manner. Can someone please write down the steps?

Can I please ask how 20C5 / 20C4 has been solved to get the fraction 16/5? I know that one way to solve this is by doing the long multiplication thing but Brunnel has calculated it in a simplified manner. Can someone please write down the steps?

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...