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Elite097
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Team A and Team B are competing against each other in a game 01 Jun 2022, 07:22
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GMATinsight avigutman ScottTargetTestPrep The question is worded as "chooses will be one of how many different possible lineups" so clearly mfmfmf can be one of 6!/3!3! lineups. I agree they have chosen mfmfmf but there is no reason to think that it means 1 specific permutation in the order mfmfmf. Ex. M1F1M2F2M3F3 being one specific permutation of mfmfmf, which can be calculated in 3!3! ways.

It can easily mean that the arrangement mfmfmf is one out of how many total arrangements i.e 6!/3!3!? Pls clarify as no explanation here seems to do the job. It easily seems to mean that mfmfmf is the chosen lineup among other possibilities
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Team A and Team B are competing against each other in a game 01 Jun 2022, 13:01
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Elite097
The question is worded as "chooses will be one of how many different possible lineups" so clearly mfmfmf can be one of 6!/3!3! lineups. I agree they have chosen mfmfmf but there is no reason to think that it means 1 specific permutation in the order mfmfmf. Ex. M1F1M2F2M3F3 being one specific permutation of mfmfmf, which can be calculated in 3!3! ways.

It can easily mean that the arrangement mfmfmf is one out of how many total arrangements i.e 6!/3!3!? Pls clarify as no explanation here seems to do the job. It easily seems to mean that mfmfmf is the chosen lineup among other possibilities
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Hi Elite097. It seems that you're struggling not with the quantitative reasoning here, but rather with the reading comprehension.
Quote:
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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In the question stem quote above, I bold-faced three words in the hopes that emphasizing them will assist you.
Once the team *has made the decision* to lineup in the particular configuration of mfmfmf, the number of possible lineups *in that particular configuration* is 3!3!.
Please let me know if you have any follow-up questions.
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Team A and Team B are competing against each other in a game 01 Jun 2022, 17:23
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Elite097
GMATinsight avigutman ScottTargetTestPrep The question is worded as "chooses will be one of how many different possible lineups" so clearly mfmfmf can be one of 6!/3!3! lineups. I agree they have chosen mfmfmf but there is no reason to think that it means 1 specific permutation in the order mfmfmf. Ex. M1F1M2F2M3F3 being one specific permutation of mfmfmf, which can be calculated in 3!3! ways.

It can easily mean that the arrangement mfmfmf is one out of how many total arrangements i.e 6!/3!3!? Pls clarify as no explanation here seems to do the job. It easily seems to mean that mfmfmf is the chosen lineup among other possibilities
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Elite097

What if I told you that out of the 262 Problem Solving questions in the 2022 OG, the 212 Problem Solving questions in the 2022 Quant Review, the 240 Data Sufficiency questions in the 2022 OG, and the 161 Data Sufficiency questions in the 2022 Quant Review, I'm pretty sure that exactly ZERO require you to actually know or use nCr OR nPr. That's 875 official questions on which they could have asked a question of that kind. But they never did. Not once. If you find one, please let me know!!

Until GMAC goes back to including even a single official question that requires either of those, my advice is not to bother with them. There are a bunch of ways those two things can be used and the number of twists and turns in a question can definitely make it so you need to understand far more nuances than are worthwhile. Every Perm/Comb question in the 2022 editions can be solved withOUT knowing anything about nCr or nPr. Formulas are great IF you know exactly when and how they can be used (and when and why they can't!), but why bother?

For this question (and for the vast majority of Perm/Comb questions), I think you're better off just reasoning through it rather than trying to employ some formula that you've memorized without TRULY understanding. BrentGMATPrepNow hit the nail on the head on this problem (and the videos in his post are definitely worth a watch if you're missing questions like this). Just work through the line in order.

First person has to be a man. How many options do we have? 3
Second person has to be a woman. How many options do we have? 3
Third has to be a man; we have two men remaining. How many options do we have? 2
Fourth has to be a woman; we have two women remaining. How many options do we have? 2
Fifth has to be a man; we have one man remaining. How many options do we have? 1
Sixth has to be a woman; we have one woman remaining. How many options do we have? 1

3*3*2*2*1*1 = 36

Answer choice D.
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Team A and Team B are competing against each other in a game 18 Sep 2023, 23:12
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This question is really confusing, it states that Team A chooses a line up of M-F-M-F-M-F and then says this line up is one of how many different possible lineups.. Doesn't that mean that this is technically 1 of 6! line ups? I'm confused, any help will be appreciated!!
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Team A and Team B are competing against each other in a game 19 Sep 2023, 00:11
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Sanaya24
This question is really confusing, it states that Team A chooses a line up of M-F-M-F-M-F and then says this line up is one of how many different possible lineups.. Doesn't that mean that this is technically 1 of 6! line ups? I'm confused, any help will be appreciated!!
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It seems you did not read the question and provided solutions carefully. The lineup is fixed as M-F-M-F-M-F. However, the men and women themselves, in their respective places, can be arranged in different ways: 3! ways for the men and 3! for the women. This results in a total of 3!*3! = 36 specific lineups.
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Team A and Team B are competing against each other in a game 29 May 2024, 21:34
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­Draw slots and fill in your options like any permutation:

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Team A and Team B are competing against each other in a game 30 May 2024, 09:02
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For anyone who has the doubt, why 720 cannot be the answer, I have spent quiet some time decoding that too. So according to my understanding, if you're someone who is selecting 6! or 720 as the answer you might be interpreting that the question is asking the total number of arrangements of lining up 3 males and 3 females. But imagine this
720 would include cases where mmfmff or mmmfff or mfmffm etc. are also possible, which is 6!/3!*3! = 20 , so for every 20 line ups there will be 36 ways (3!*3!) ways in which the males and females will be arranged.

So either it was interpreted as mfmfmf out of 20 different combinations or 36 ways of arranging mfmfmf.
20 is anyway to part of the answer choices.
Hence Ans D.­
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Team A and Team B are competing against each other in a game 01 Oct 2024, 05:45
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This question is very confusing and its because its hard to determine what the question means by the term "lineups" at the end of the last sentence. Is "lineups" referring to all the different ways that the specific MALES and FEMALES can be arranged in the predetermined MFMFMF set up, or does "lineups" mean all the possible ways to arrange the genders, as in MMMFFF, MFMMFF, etc. It doesn't explicitly say which "lineups" its referring to.

"The lineup that Team A chooses will be one of how many different possible lineups" could just as easily mean TEAM A chose MFMFMF out of all the possible lineups that the genders could have been arranged. They chose MFMFMF out of MMFFMF, MMMFFF, FFFMMM, etc. and how many of those COULD they have chosen?

OR

It could mean that TEAM A already chose MFMFMF as their predetermined set up and the question wants to know how many different arrangements you can put the specific males and females in that specific "lineup".

IMO the language isn't clear.
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Team A and Team B are competing against each other in a game 16 Nov 2024, 07:34
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Hey Bunuel,

A small clarification is required please - In GMAT, how do we infer whether the objects provided in the question stem are identical or not. For ex- in here, it could have been the case that all 3 Males are identical & 3 Females are identical.
Does this mean, the question will explicitly state that Males are identical and so on?
I face this constraint confusion always whenever objects are involved which may or may not be identical. Since we only divide when there is an identical number of objects. If 3 males and 3 females were identical, we would have divided by 3!3!.
Please guide me here.
Thanks a ton :)
Bunuel
Raihanuddin

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.

Please clarify the confusion.

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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Team A and Team B are competing against each other in a game 16 Nov 2024, 07:40
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saransh2797
Hey Bunuel,

A small clarification is required please - In GMAT, how do we infer whether the objects provided in the question stem are identical or not. For ex- in here, it could have been the case that all 3 Males are identical & 3 Females are identical.
Does this mean, the question will explicitly state that Males are identical and so on?
I face this constraint confusion always whenever objects are involved which may or may not be identical. Since we only divide when there is an identical number of objects. If 3 males and 3 females were identical, we would have divided by 3!3!.
Please guide me here.
Thanks a ton :)
Bunuel
Raihanuddin

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.

Please clarify the confusion.

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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Where clarification is necessary, it will be given. If it's not explicitly stated and the context doesn’t make it clear, use common sense: people are distinct, so their individual positioning changes the lineup, meaning order matters.
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Team A and Team B are competing against each other in a game 09 Jan 2025, 05:37
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ganand
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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The question is relatively easy, could be solved in 10 seconds , use fill in the blanks methods,,,, MFMFMF,,,,, so 3 gaps of M, 3 of F,,,,3*3*2*2*1*1=36 ways simple
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Team A and Team B are competing against each other in a game 17 Jan 2025, 03:33
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ganand
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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To determine the number of possible lineups for Team A, where 3 males (M) and 3 females (F) are arranged in an alternating pattern (M, F, M, F, M, F), we can follow these steps:
  1. Arrange the Males: The 3 males can be arranged in the 3 male positions in 3!3!3! (3 factorial) ways. Calculating 3!3!3!:
    3!=3×2×1=63! = 3 \times 2 \times 1 = 63!=3×2×1=6
  2. Arrange the Females: Similarly, the 3 females can be arranged in the 3 female positions in 3!3!3! ways. Calculating 3!3!3!:
    3!=3×2×1=63! = 3 \times 2 \times 1 = 63!=3×2×1=6
  3. Total Arrangements: Since the arrangements of males and females are independent, the total number of lineups is the product of the two arrangements:
    3!×3!=6×6=363! \times 3! = 6 \times 6 = 363!×3!=6×6=36
Therefore, the total number of different possible lineups for Team A is 36.
Answer: (D) 36
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Team A and Team B are competing against each other in a game 09 Apr 2026, 23:42
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This Question is very confusing. One could find a difference between
"how many different possible lineups?" and "how many different possible lineups from the given lineup?"

Can one tell if this is an actual gmat question please?
ganand
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
Show more
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Team A and Team B are competing against each other in a game 10 Apr 2026, 03:47
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tryorcry
This Question is very confusing. One could find a difference between
"how many different possible lineups?" and "how many different possible lineups from the given lineup?"

Can one tell if this is an actual gmat question please?

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Yes, this is an official GMAT question:



Please review the discussion. This question has already been discussed in quite a bit of detail in the thread.
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Team A and Team B are competing against each other in a game 10 Apr 2026, 06:18
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I understand this is an official question but I still have my doubts.
It says one of how many possible lineups and calls the aforementioned lineup as "one".
So one of how many total could mean how many such blueprints possible? Or how many kinds of lineups possible with one being M,F,M,F,M,F?
In that case shouldn't it be 6!/3!*3! = 20? Kindly help me out.

PS:- Yes I read the thread as well but I am not satisfied.
Let me try rephrasing it again:
" The lineup that Team A chooses will be one of how many different possible lineups?"
This in other words IMO says, the lineup that team A chooses = M,F,M,F,M,F is one out of how many different "possible" lineups.
It calls that setup a "lineup" so the number of lineups must technically be the numbers of ways of having an M,F combo arranged in different ways right?
If it were like how the answer is, it should be like how many different possible arrangement of the lineup are there, or something like that?
Quote:


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