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Team A and Team B are competing against each other in a game

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New post 29 May 2017, 03:38
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Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

(A) 9
(B) 12
(C) 15
(D) 36
(E) 720
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 27 Jun 2017, 15:16
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ganand wrote:
Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

(A) 9
(B) 12
(C) 15
(D) 36
(E) 720


Take the task of lining up the 6 competitors and break it into stages.

Stage 1: Select a competitor for the 1st position
This person must be a male.
Since there are 3 males to choose from, we can complete stage 1 in 3 ways

Stage 2: Select a competitor for the 2nd position
This person must be a female.
Since there are 3 females to choose from, we can complete stage 2 in 3 ways

Stage 3: Select a competitor for the 3rd position
This person must be a male.
There are 2 males remaining to choose from (since we already selected a male in stage 1), so we can complete stage 3 in 2 ways

Stage 4: Select a competitor for the 4th position
This person must be a female.
There are 2 females remaining to choose from. So we can complete stage 4 in 2 ways

Stage 5: Select a male for the 5th position
There's only 1 male remaining. So we can complete stage 5 in 1 way

Stage 6: Select a female for the 6th position
There's only 1 female remaining. So we can complete stage 6 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus create a 6-person lineup) in (3)(3)(2)(2)(1)(1) ways (= 36 ways)

Answer:

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Team A and Team B are competing against each other in a game  [#permalink]

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New post 11 Jul 2017, 01:30
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ashygoyal wrote:
Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

(A) 9
(B) 12
(C) 15
(D) 36
(E) 720

I have a doubt here.
Should we count,
(m1 w1 m2 w2 m3 w3) as a line up or,
(m w m w m w) as a line up?

According to the question, it says one of the lineups is (m w m w m w)
Doesn't that mean, other lineups will also include (m m m w w w), (w w w m m m),... and so on?

What wording in question makes us stick to only (m w m w m w)?

Please correct if my thought process is wrong.


Regards,
Ashygoyal


The question says that the lineup should be male, female, male, female, male, female (M-F-M-F-M-F) only. So, alternating males and females, starting with a male. Any male can take any of the three M's positions and any female can take any of the three F's positions giving different arrangements. 3 men can be arranged in 3! ways and similarly 3 women can be arranged in 3! ways. So, the answer is 3!*3! = 36.

Answer: D.

Hope it's clear.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 29 May 2017, 03:54
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There is only one way of forming the line MFMFMF.
However, there are 3! ways of arranging the men in the line
If there are 3 men (M1,M2,M3)
the ways they can be arranged are:
1st 2nd 3rd
M1-M2- M3
M1- M3- M2
M2- M1- M3
M2- M3- M1
M3- M1- M2
M3- M2- M1(Total 6 ways)

Similarly women can also be arranged in 6 ways.

Total possibilities of arranging both men and women are 6*6*1 = 36 ways(Option D)
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 29 May 2017, 03:57
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Men have to occupy 1st, 3rd and 5th positions. This can be done in 3*2*1 = 6 ways
Women have to occupy 2nd, 4th and 6th positions. This can be done in 3*2*1 = 6 ways

Together, the above two things have to be done which can be done in 6*6 = 36 ways

Hence D answer
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 29 May 2017, 03:58
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Please correct me if i am wrong

M1, M2, M3, F1, F2, F3 can be arranged in 6! ways


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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 29 May 2017, 04:19
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mynamegoeson wrote:
Please correct me if i am wrong

M1, M2, M3, F1, F2, F3 can be arranged in 6! ways


Sent from my iPhone using GMAT Club Forum


Hi

when you say 6!, you are listing ALL the possible arrangements of 3 men and 3 women in a straight line.
But as per the question, we have constraints. Men can occupy only 1st, 3rd, 5th places from start while women can occupy only 2nd, 4th, 6th places from start.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 10 Jul 2017, 13:23
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amanvermagmat wrote:
mynamegoeson wrote:
Please correct me if i am wrong

M1, M2, M3, F1, F2, F3 can be arranged in 6! ways


Sent from my iPhone using GMAT Club Forum


Hi

when you say 6!, you are listing ALL the possible arrangements of 3 men and 3 women in a straight line.
But as per the question, we have constraints. Men can occupy only 1st, 3rd, 5th places from start while women can occupy only 2nd, 4th, 6th places from start.


I have a doubt here.
Should we count,
(m1 w1 m2 w2 m3 w3) as a line up or,
(m w m w m w) as a line up?

According to the question, it says one of the lineups is (m w m w m w)
Doesn't that mean, other lineups will also include (m m m w w w), (w w w m m m),... and so on?

What wording in question makes us stick to only (m w m w m w)?

Please correct if my thought process is wrong.


Regards,
Ashygoyal
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 10 Jul 2017, 14:59
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The question is really confusing. It's not clear if the suggested approach to line up 3 males and 3 females is a pattern or just one of the possible solutions.
I also resolved it through 6! as the questions asked " The lineup that Team A chooses will be one of how many different possible lineups"

Even if you google the question you will find a google book, and the response is still confusing:)) It says Any of the 3 males can be first in the line and any of the 3 females can be second
But why not the females start the line? I cannot find this constraint in the question
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 11 Jul 2017, 06:51
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Bunuel wrote:

The question says that the lineup should be male, female, male, female, male, female (M-F-M-F-M-F) only. So, alternating males and females, starting with a male. Any male can take any of the three M's positions and any female can take any of the three F's positions giving different arrangements. 3 men can be arranged in 3! ways and similarly 3 women can be arranged in 3! ways. So, the answer is 3!*3! = 36.

Answer: D.

Hope it's clear.


Sorry Bunuel, I would disagree, the question doesn't say should be made and only it clearly says
Quote:
Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female
that's why so many people found it's confusing.
I get it, GMAT candidates should learn the GMAT language otherwise risk of failure on such questions is high.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 11 Jul 2017, 07:12
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cbh wrote:
Bunuel wrote:

The question says that the lineup should be male, female, male, female, male, female (M-F-M-F-M-F) only. So, alternating males and females, starting with a male. Any male can take any of the three M's positions and any female can take any of the three F's positions giving different arrangements. 3 men can be arranged in 3! ways and similarly 3 women can be arranged in 3! ways. So, the answer is 3!*3! = 36.

Answer: D.

Hope it's clear.


Sorry Bunuel, I would disagree, the question doesn't say should be made and only it clearly says
Quote:
Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female
that's why so many people found it's confusing.
I get it, GMAT candidates should learn the GMAT language otherwise risk of failure on such questions is high.


In this context "decides to lineup" = " should lineup".
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 11 Jul 2017, 08:17
M1 F1 M2 F2 M3 F3

possibilities for M1 is 3, for M2 is 2 M3 is 1 ,,,total 3*2 = 6
same for females..hence total ways 6 * 6 = 36
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 12 Jul 2017, 17:12
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ganand wrote:
Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

(A) 9
(B) 12
(C) 15
(D) 36
(E) 720


We need to determine the number of ways to lineup male, female, male, female, male, female.

Since there are 3 males, we have 3 options for the first spot, and since there are 3 females, we have 3 options for the second spot. Then we have 2 options for the third spot, 2 options for the fourth, and 1 option for each of the last two spots. Thus, the number of ways to lineup that group is 3 x 3 x 2 x 2 x 1 x 1 = 36.

Answer: D
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 05 Nov 2017, 18:22
ganand wrote:
Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

(A) 9
(B) 12
(C) 15
(D) 36
(E) 720


Line up - M1 F1 M2 F2 M3 F3;
M1 can be any of the 3 males - 3 choices
M2 can be any of the 2 remaining males - 2 choices
M3 has to be the last male - 1 choice
Therefore the total arrangement for males = 3 * 2 * 1 = 6
Similarly,
F1 can be any of the 3 females - 3 choices
F2 can be any of the 2 remaining females - 2 choices
F3 has to be the last female - 1 choice
Therefore the total arrangement for females = 3 * 2 * 1 = 6
Now the total arrangement possible = 6 * 6 = 36

OR

3 males and 3 females can be arranged in 6! ways = 720 ways
but the arrangement has to be M F M F M F. This arrangement can happen in 6!/3!*3! ways = 20 ways
Hence the total ways = 20/720 = 1/36
But to get this unique combination of M1 F1 M2 F2 M3 F3 we should have the numerator as 1.
Hence, 36 ways.

Option D
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 06 Nov 2017, 20:51
Bunuel wrote:
cbh wrote:
Bunuel wrote:

The question says that the lineup should be male, female, male, female, male, female (M-F-M-F-M-F) only. So, alternating males and females, starting with a male. Any male can take any of the three M's positions and any female can take any of the three F's positions giving different arrangements. 3 men can be arranged in 3! ways and similarly 3 women can be arranged in 3! ways. So, the answer is 3!*3! = 36.

Answer: D.

Hope it's clear.


Sorry Bunuel, I would disagree, the question doesn't say should be made and only it clearly says
Quote:
Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female
that's why so many people found it's confusing.
I get it, GMAT candidates should learn the GMAT language otherwise risk of failure on such questions is high.


In this context "decides to lineup" = " should lineup".


For me, the last line of the question created the confusion.

"The lineup that Team A chooses will be one of how many different possible lineups?"

So I though M F M F M F was one kind of line up and hence I found the other type of line ups using 6!. Understanding such questions become really difficult during the exam.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 05 Jan 2018, 06:33
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I also got confused by the wording of the question.



Just for curiosity, if the question were implying that the lineup M F M F M F was not a patter to follow but only one of the many possible lineups (ways) in which a man and a woman can be arranged, would the solution be 6! / (3!·3!) = 20? Since we are arranging 6 objects with 3 of them alike.



Please, correct me if I´m wrong.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 21 Jan 2018, 08:29
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As it is written only Males and Females, how do we know that the order matters? Shouldn't we divide it by (3*2*1) twice?
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 10 Jun 2018, 02:41
Hi Bunuel,
where does it state in the question that the lineups MUST start with a male? It is just stated that Team A chooses M-F-M-F-M-F. If this is one of all possible lineups, Team A could also start with a female (F-M-F-M-F-M therefore IS a possible lineup). What I mean is "the option" to start with F is there, it's not discarded in the question stem.

What am I not seeing?

Thanks!
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 10 Jun 2018, 02:57
pkloeti wrote:
Hi Bunuel,
where does it state in the question that the lineups MUST start with a male? It is just stated that Team A chooses M-F-M-F-M-F. If this is one of all possible lineups, Team A could also start with a female (F-M-F-M-F-M therefore IS a possible lineup). What I mean is "the option" to start with F is there, it's not discarded in the question stem.

What am I not seeing?

Thanks!


Check the highlighted part of the stem:

Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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New post 10 Jun 2018, 03:16
Check the highlighted part of the stem:

Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?[/quote]

So does this mean in "GMAT language" that every 1st, 3rd and 5th person in the lineup MUST be a male? If so, I get it. I guess it's about practicing GMAT language...
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Re: Team A and Team B are competing against each other in a game   [#permalink] 10 Jun 2018, 03:16

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