GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Apr 2020, 16:08

### GMAT Club Daily Prep

#### 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

# In a group of 8 semifinalists, all but 2 will advance to the final rou

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62619
In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

22 May 2016, 13:46
1
15
00:00

Difficulty:

95% (hard)

Question Stats:

32% (01:30) correct 68% (01:48) wrong based on 171 sessions

### HideShow timer Statistics

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

_________________
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Aug 2009
Posts: 8314
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

22 May 2016, 19:26
3
3
Bunuel wrote:
In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Hi,

there are two points to remember-

1) Is it important here that how many go into finals... NO....
what is important is HOW many get medals..3
finally these 3 can be any of the 8 - $$8C3 = \frac{8!}{5!3!} = \frac{8*7*6}{3*2}=56$$

2) Is order important...NO
we are looking for groups only..

ans 56
B
_________________
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 62619
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

03 Jul 2017, 01:30
3
Palaksehgal3 wrote:
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?

Yes, but initial number is still 8. Do we know which 2 won't advance to the final? No. So, the size of the group we are selecting from is still 8.

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Intermediary step about "all but 2 will advance to the final round" is just to confuse us: any group of 3 is equally likely to win, so we can skip this part and directly calculate ways to choose 3 contestants out of 8: $$C3_8=56$$.

Answer: B.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 62619
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

03 Jul 2017, 01:44
2
2
Palaksehgal3 wrote:
Bunuel wrote:
Palaksehgal3 wrote:
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?

Yes, but initial number is still 8. Do we know which 2 won't advance to the final? No. So, the size of the group we are selecting from is still 8.

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Intermediary step about "all but 2 will advance to the final round" is just to confuse us: any group of 3 is equally likely to win, so we can skip this part and directly calculate ways to choose 3 contestants out of 8: $$C3_8=56$$.

Answer: B.

Makes sense. Thanks Bunuel
I am having a hard time with probability and permutations. Could you please advise how to go about improving at it?

Check the links below:
Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Tough and tricky questions on Combinations

Probability Made Easy!

Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.
_________________
Manager
Joined: 19 Aug 2015
Posts: 82
Location: India
GMAT 1: 650 Q49 V30
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

09 Jun 2017, 09:11
For this problem we have to select 3 semifinalists out of 8 so
$$8_C_3$$
Answer B
Intern
Joined: 30 Mar 2017
Posts: 8
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

03 Jul 2017, 01:15
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?
Intern
Joined: 30 Mar 2017
Posts: 8
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

03 Jul 2017, 01:42
Bunuel wrote:
Palaksehgal3 wrote:
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?

Yes, but initial number is still 8. Do we know which 2 won't advance to the final? No. So, the size of the group we are selecting from is still 8.

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Intermediary step about "all but 2 will advance to the final round" is just to confuse us: any group of 3 is equally likely to win, so we can skip this part and directly calculate ways to choose 3 contestants out of 8: $$C3_8=56$$.

Answer: B.

Makes sense. Thanks Bunuel
I am having a hard time with probability and permutations. Could you please advise how to go about improving at it?
Intern
Joined: 23 May 2019
Posts: 33
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

21 Jan 2020, 06:23
Bunuel wrote:
Palaksehgal3 wrote:
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?

Yes, but initial number is still 8. Do we know which 2 won't advance to the final? No. So, the size of the group we are selecting from is still 8.

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Intermediary step about "all but 2 will advance to the final round" is just to confuse us: any group of 3 is equally likely to win, so we can skip this part and directly calculate ways to choose 3 contestants out of 8: $$C3_8=56$$.

Answer: B.

Why is 8c6 * 6c3 wrong ? In this ,we are selecting 6 persons out of 8 as 2 will not advance to the final round.

Posted from my mobile device
Intern
Joined: 16 Jul 2018
Posts: 3
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

25 Jan 2020, 09:04
Bunuel wrote:
Palaksehgal3 wrote:
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?

Yes, but initial number is still 8. Do we know which 2 won't advance to the final? No. So, the size of the group we are selecting from is still 8.

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Intermediary step about "all but 2 will advance to the final round" is just to confuse us: any group of 3 is equally likely to win, so we can skip this part and directly calculate ways to choose 3 contestants out of 8: $$C3_8=56$$.

Answer: B.

[color=#ff0000]
why 8C6 x 6C3 is wrong??
[/color]
Intern
Joined: 27 Nov 2017
Posts: 5
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

### Show Tags

25 Jan 2020, 18:15
aarushisingla wrote:
Bunuel wrote:
Palaksehgal3 wrote:
As per the question, only 6 semifinalists made it to the 3rd round.
So why is the answer not 6c3?

Yes, but initial number is still 8. Do we know which 2 won't advance to the final? No. So, the size of the group we are selecting from is still 8.

In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?

(A) 20
(B) 56
(C) 120
(D) 560
(E) 720

Intermediary step about "all but 2 will advance to the final round" is just to confuse us: any group of 3 is equally likely to win, so we can skip this part and directly calculate ways to choose 3 contestants out of 8: $$C3_8=56$$.

Answer: B.

Why is 8c6 * 6c3 wrong ? In this ,we are selecting 6 persons out of 8 as 2 will not advance to the final round.

Posted from my mobile device

Yea, this is what I did as well. :/
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou   [#permalink] 25 Jan 2020, 18:15
Display posts from previous: Sort by

# In a group of 8 semifinalists, all but 2 will advance to the final rou

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne