Last visit was: 11 Sep 2024, 08:58 It is currently 11 Sep 2024, 08:58
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 17 May 2015
Posts: 198
Own Kudos [?]: 3219 [396]
Given Kudos: 85
Manager
Joined: 24 Jun 2017
Posts: 87
Own Kudos [?]: 170 [71]
Given Kudos: 130
Math Expert
Joined: 02 Sep 2009
Posts: 95451
Own Kudos [?]: 657644 [66]
Given Kudos: 87242
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19440
Own Kudos [?]: 23184 [34]
Given Kudos: 286
Location: United States (CA)
Re: Team A and Team B are competing against each other in a game [#permalink]
23
Kudos
11
Bookmarks
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.

General Discussion
CEO
Joined: 26 Feb 2016
Posts: 2863
Own Kudos [?]: 5406 [16]
Given Kudos: 47
Location: India
GPA: 3.12
Re: Team A and Team B are competing against each other in a game [#permalink]
11
Kudos
5
Bookmarks
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)
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2583 [4]
Given Kudos: 459
Location: India
Re: Team A and Team B are competing against each other in a game [#permalink]
2
Kudos
2
Bookmarks
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

Current Student
Joined: 18 Aug 2016
Posts: 531
Own Kudos [?]: 599 [3]
Given Kudos: 198
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: Team A and Team B are competing against each other in a game [#permalink]
3
Kudos
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
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2583 [4]
Given Kudos: 459
Location: India
Re: Team A and Team B are competing against each other in a game [#permalink]
4
Kudos
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.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31270 [63]
Given Kudos: 799
Re: Team A and Team B are competing against each other in a game [#permalink]
29
Kudos
34
Bookmarks
Top Contributor
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)

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

RELATED VIDEOS

Intern
Joined: 16 Feb 2016
Posts: 21
Own Kudos [?]: 26 [8]
Given Kudos: 21
Re: Team A and Team B are competing against each other in a game [#permalink]
8
Kudos
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
Manager
Joined: 24 Jun 2017
Posts: 87
Own Kudos [?]: 170 [6]
Given Kudos: 130
Re: Team A and Team B are competing against each other in a game [#permalink]
6
Kudos
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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 95451
Own Kudos [?]: 657644 [3]
Given Kudos: 87242
Re: Team A and Team B are competing against each other in a game [#permalink]
3
Kudos
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.

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".
Intern
Joined: 12 Jan 2018
Posts: 4
Own Kudos [?]: 4 [3]
Given Kudos: 15
Re: Team A and Team B are competing against each other in a game [#permalink]
3
Kudos
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!
Math Expert
Joined: 02 Sep 2009
Posts: 95451
Own Kudos [?]: 657644 [0]
Given Kudos: 87242
Re: Team A and Team B are competing against each other in a game [#permalink]
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?
Intern
Joined: 12 Jan 2018
Posts: 4
Own Kudos [?]: 4 [0]
Given Kudos: 15
Re: Team A and Team B are competing against each other in a game [#permalink]
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...
Math Expert
Joined: 02 Sep 2009
Posts: 95451
Own Kudos [?]: 657644 [1]
Given Kudos: 87242
Re: Team A and Team B are competing against each other in a game [#permalink]
1
Kudos
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.
Manager
Joined: 11 Sep 2013
Posts: 90
Own Kudos [?]: 575 [1]
Given Kudos: 381
Concentration: Finance, Finance
Re: Team A and Team B are competing against each other in a game [#permalink]
1
Kudos
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.

Math Expert
Joined: 02 Sep 2009
Posts: 95451
Own Kudos [?]: 657644 [4]
Given Kudos: 87242
Re: Team A and Team B are competing against each other in a game [#permalink]
2
Kudos
2
Bookmarks
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.
Intern
Joined: 23 Oct 2020
Posts: 21
Own Kudos [?]: 4 [0]
Given Kudos: 47
Re: Team A and Team B are competing against each other in a game [#permalink]
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.

Bunuel chetan2u why can't we use the classic formula for arrangements here "6!/3!*3!" ??
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11513
Own Kudos [?]: 35938 [3]
Given Kudos: 333
Re: Team A and Team B are competing against each other in a game [#permalink]
3
Kudos
Michele4 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.

$$\frac{6!}{3!3!}$$ is the formula to arrange 6 things out of which 3 are of one kind and the other 3 are of the other kind.