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
Elite097What 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.