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

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Math Expert
Joined: 02 Sep 2009
Posts: 61283
In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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

Difficulty:

95% (hard)

Question Stats:

32% (01:30) correct 68% (01:48) wrong based on 168 sessions

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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

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Math Expert
Joined: 02 Aug 2009
Posts: 8261
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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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
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##### General Discussion
Manager
Joined: 19 Aug 2015
Posts: 84
Location: India
GMAT 1: 650 Q49 V30
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 61283
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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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: $$C3_8=56$$.

_________________
Intern
Joined: 30 Mar 2017
Posts: 8
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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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: $$C3_8=56$$.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 61283
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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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: $$C3_8=56$$.

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?

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Tough and tricky questions on Combinations

Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.
_________________
Intern
Joined: 23 May 2019
Posts: 27
Re: In a group of 8 semifinalists, all but 2 will advance to the final rou  [#permalink]

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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: $$C3_8=56$$.

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]

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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: $$C3_8=56$$.

[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]

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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: $$C3_8=56$$.

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
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