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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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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!!

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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­Draw slots and fill in your options like any permutation:

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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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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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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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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.

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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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
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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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
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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