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

Hi Elite097. It seems that you're struggling not with the quantitative reasoning here, but rather with the reading comprehension.

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.

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.

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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Given: 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.
Asked: The lineup that Team A chooses will be one of how many different possible lineups?

Number of ways to arrange males in given locations = 3! = 6
Number of ways to arrange females in given locations = 3! = 6
Number of different lineups possible = 3!*3! = 6*6 = 36

IMO D

Honestly, this is just an unclear question. And apparently noone here was also able to clearly falsify the interpretation that MFMFMF is a possible option, simply because the question is ambiguous.

The only argument that speaks for the intended interpretation is why they would provide the order MFMFMF if it was not relevant to the question. But there are plenty of other questions that contain filler data only for the sake of confusion, so this does not count.

Just imagine the answer to this question was actually 6!/3!3!=20, would you have to make any change to the question in order to derive this conclusion? I personally cannot think of one.

Btw ChatGPT4 amusingly also calculated 6!/3!3!=20, I know that this does not prove anything, but it should make you think.

I understand that the number of ways this alignment can be done is 3*3*2*2*1*1 = 36

However, as the question asks 'The lineup that Team A chooses will be one of how many different possible lineups?', it seems like we are asked out of all the different combinations, what is the proportion that these combinations take ?

The total number of ways without considering the male-female alignment would then be 6! = 720
The answer would then be 36/720 = 1/20...