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

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Math Expert
Joined: 02 Sep 2009
Posts: 62455
Re: Team A and Team B are competing against each other in a game  [#permalink]

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10 Jun 2018, 02:18
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pkloeti wrote:
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?

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...[/quote]

Well, yes. How else? The stem directly specifies the desired line-up: it should start with a male and then alternate females and males.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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10 Jun 2018, 02:24
Bunuel wrote:
pkloeti wrote:
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?

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...

Well, yes. How else? The stem directly specifies the desired line-up: it should start with a male and then alternate females and males.[/quote]

OK, thanks a lot!!
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Joined: 11 Sep 2013
Posts: 131
Concentration: Finance, Finance
Team A and Team B are competing against each other in a game  [#permalink]

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09 Sep 2018, 09:31
Bunuel wrote:
pkloeti wrote:
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?

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...

Well, yes. How else? The stem directly specifies the desired line-up: it should start with a male and then alternate females and males.[/quote]

Hi Bunuel,

Could you please clarify me the following? the

I was also confused by the wording. But I was sure that it won't be 6! ways because MMMFFF can't be arranged in 6! ways.

I thought it would be 6!/(3!*3!) = 20

But this option is not given. So, I had to figure out the solution by doing 3!*3! = 36

Now, I am not sure what the difference is between 6!/(3!*3!) = 20 and 3!*3! = 36.

I think 6!/(3!*3!) = 20 means the number of the different possible combination. and

3!*3! = 36 means the arrangement with a certain condition.

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Joined: 02 Sep 2009
Posts: 62455
Team A and Team B are competing against each other in a game  [#permalink]

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09 Sep 2018, 19:53
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1
Raihanuddin wrote:
Hi Bunuel,

Could you please clarify me the following? the

I was also confused by the wording. But I was sure that it won't be 6! ways because MMMFFF can't be arranged in 6! ways.

I thought it would be 6!/(3!*3!) = 20

But this option is not given. So, I had to figure out the solution by doing 3!*3! = 36

Now, I am not sure what the difference is between 6!/(3!*3!) = 20 and 3!*3! = 36.

I think 6!/(3!*3!) = 20 means the number of the different possible combination. and

3!*3! = 36 means the arrangement with a certain condition.

3!*3! is the number of permutations when the lineup is male, female, male, female, male, female (M-F-M-F-M-F) only.

6!/(3!3!) is the number of permutations of 3 males and 3 females without any restrictions.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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09 Sep 2018, 20:06
Bunuel wrote:
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.

Hope it's clear.

Posted from my mobile device

Can't we consider total combinations as 6!/(3!×3!) which gives 20. In this case with total combinations being 20, how can a specific combination gives 36 ?
Math Expert
Joined: 02 Sep 2009
Posts: 62455
Re: Team A and Team B are competing against each other in a game  [#permalink]

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09 Sep 2018, 20:10
anvesh004 wrote:
Bunuel wrote:
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.

Hope it's clear.

Posted from my mobile device

Can't we consider total combinations as 6!/(3!×3!) which gives 20. In this case with total combinations being 20, how can a specific combination gives 36 ?

I think you did not read the whole discussion. Please do. I hope it helps.
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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09 Nov 2019, 13:08
What is a tug-of-war game and why do they mention team B? Does team B have anything to do with this? Thanks!
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Re: Team A and Team B are competing against each other in a game  [#permalink]

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26 Nov 2019, 08:01
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

total males = 3 and females = 3
line up male, female, male, female, male, female = 3*3*2*2*1*1 ; 36
IMO D
Re: Team A and Team B are competing against each other in a game   [#permalink] 26 Nov 2019, 08:01

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