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:

73% (00:43) correct 27% (00:44) wrong based on 146 sessions

HideShow timer Statistics

Tough and Tricky questions: Combinations.

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

Re: Four contestants representing four different countries advance to the [#permalink]

Show Tags

08 Dec 2014, 07:24

1

This post received KUDOS

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

A) 6 B) 7 C) 12 D) 16 E) 24

Number of ways First-place medal can be awarded to four contestants = 4 Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3

Therefore number of possibilities = 4 *3 =12 Answer: C

Re: Four contestants representing four different countries advance to the [#permalink]

Show Tags

08 Dec 2014, 20:11

1

This post received KUDOS

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

We have 2 slots to be filled using 4 contestants: 4 options for slot1 * 3 option for slot2 = 4* 3 = 12

Ans. C) 12
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

A) 6 B) 7 C) 12 D) 16 E) 24

isnt 4C2 (i.e 6 ways) the answer ? please clarify

Thanks

No. 4C2 gives the number of two-contestant groups possible from 4. Suppose we are choosing group {A, B}. We can have A = first-place and B = second-place or vise-versa, so for each group there are 2 possible arrangement with respect to how a first-place and second-place medal can be awarded. Therefore the answer is 4C2*2 = 12.

Re: Four contestants representing four different countries advance to the [#permalink]

Show Tags

20 Dec 2014, 20:57

Bunuel wrote:

vinbitstarter wrote:

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

A) 6 B) 7 C) 12 D) 16 E) 24

isnt 4C2 (i.e 6 ways) the answer ? please clarify

Thanks

No. 4C2 gives the number of two-contestant groups possible from 4. Suppose we are choosing group {A, B}. We can have A = first-place and B = second-place or vise-versa, so for each group there are 2 possible arrangement with respect to how a first-place and second-place medal can be awarded. Therefore the answer is 4C2*2 = 12.

Answer: C.

Hope it's clear.

Yes, thank you another way to look at it is : 4C1 * 3C1 = 12 possible ways.

Re: Four contestants representing four different countries advance to the [#permalink]

Show Tags

26 Dec 2014, 01:39

Hi,

Let me share the 2 ways in which I did it. Please, let me know if there is a mistake somewhere in my thinking or a possible trap in these 2 solutions:

1st solution: 4!=24 possible ways 24/2=12, because it is the first 2 spots that will be changing. It is sort of intuitive, so it could easily be wrong...

I tried the 2nd solution solution, just to see if I end up with 12 again: We have A - B - C - D as the possible slots. The first 2 slots can change so that it is occupied by 2 different people. Starting with A we have: A - B - C - D A - C - B - D A - D - B - C So, these are 3 ways, only taking into account A. We gave 4 different people, so 3 X 4 = 12 (just thinking that each one of them should have the same chances).

Re: Four contestants representing four different countries advance to the [#permalink]

Show Tags

04 Sep 2017, 07:11

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.
_________________