When one person is selected for the committee, there will be 9 left to be chosen next. 8 out of 9 will not be married to the selected person, so the probability of selecting someone else=8/9.
So there are now 8 people left from which to choose the next committee member. 6 out of 8 will not be married to either of the two selected members, so now we have (8/9)(6/8)=2/3 as the probability that none of the three selected people will be married to one of the others. There are now 7 remaining people, including the 3 spouses of those selected, so 4/7 will not be married to any of those selected making the final probability:
(2/3)(4/7)=8/21.
The committee now has 4 people and the 6 remaining people include the 4 spouses of those selected.