Using a more indirect method, you can subtract out the undesirable outcomes from the total number of outcomes to get the desired outcomes.

In this case, the undesired outcome is having a married couple out of the three spots in the committee.

There are a total of 10 people to choose from (5 couples).
Order doesn't matter (A group of Person 1, Person 2, and Person 3 is the same group as Person 2, Person 1, and Person 3), so we use combinations.

10 Choose 3 = \(\frac{10*9*8}{3*2} = 5*3*8 = 120\)

So if there were no restrictions, the total number of outcomes would be 120 different committees.

Now consider the undesired outcomes: choosing a married couple for 2 of the 3 spots on the committee.

Since there are 5 couples, if we choose 1 couple (2 people) to fill two spots, we could choose any of the remaining 8 people to fill the third spot.
That's 8 different combinations for each of the 5 couples. So there are 40 different committees that include a married couple.

The total number of undesired outcomes then is 40.

Now we subtract: 120-40 = 80, giving us our answer of D.

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