Ah--in that case, the question relies on a critical assumption: that couples don't necessarily stay together.

The analysis above assumes that couples stay together.

But if couples do not stay together, then a lot more possibilities exist:

You can have 1 married person, and 3 singles.

You can have 2 married people, and 2 singles.

You can have 3 married people, and 1 single.

You can have 4 married people (only 2 of them can be a couple, the other 2 cannot).

So this complicates things further. In this case, using the method maliyeci and yogibearsayshi suggested above, you find the total possible combinations and then subtract the 1 case scenario that is prohibited.

So you treat the married people like singles in terms of calculations, but then subtract out the case when there are 2 married couples.

So yes, that would be 10C4 - 3C2.

10C4 because you are selecting from 10 and choosing 4 people (regardless of married/single status).

3C2 because you want the # of people possibilities for 2 married couples that you want to subtract from the overall.

This would give you:

10C4 = 10! / (4! * 6!) = (10*9*8*7) / (4*3*2*1) = (10*3*7) / (1) = 210

3C2 = 3! / (2! * 1*) = 3

210 - 3 = 207

I'm not so sure you'd see a question worded like this on the actual GMAT. The calculation with the factorials is a little bit more in depth than I would expect. But good to go through though.

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