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 350,000 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:

Judges will select 5 finalists from the 7 contestants [#permalink]
17 Jan 2005, 13:39

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

Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?

I also figured another approach to this. The whole logic of selecting 5 out of 7 is just to throw us in a loop. In the end, there will be three candidates from the 7 to get the prizes.

However since order matters, its a permuation issue.
i.e: 7 possible choices for 1st place, 6 for second and 5 for third.

I also figured another approach to this. The whole logic of selecting 5 out of 7 is just to throw us in a loop. In the end, there will be three candidates from the 7 to get the prizes.

However since order matters, its a permuation issue. i.e: 7 possible choices for 1st place, 6 for second and 5 for third.

So total possible arrangement = 7*6*5=210

thats an easier and much clearer route to take.. Gayathri...thanks..

Well i can explain why the answer is 210.
The principle of choice is being tested here and i think here it goes:

First out of 5 finalist out of 7 contestants are selected, meaning order does not matter it's just 5 people from 7 people thus we use 7C5 and we get 21

Then out of these 5, 3 contestants are ranked such that: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place (this means order matters because it asks for different "arrangement" of prize winners) thus we use 5P3 and we get 10.

Well i can explain why the answer is 210. The principle of choice is being tested here and i think here it goes:

First out of 5 finalist out of 7 contestants are selected, meaning order does not matter it's just 5 people from 7 people thus we use 7C5 and we get 21

Then out of these 5, 3 contestants are ranked such that: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place (this means order matters because it asks for different "arrangement" of prize winners) thus we use 5P3 and we get 10.

21 * 10 = 210

Folaa3, what do u think if within 3 contestants A,B,C, the order can change, first A, second B, third C or first B, second C, third A. So # of ways to arrange 3 best winners are 3!