A hint to get started
Choose a committee subject to a married-couple restriction
A committee of 3 people is to be chosen from 4 married couples. Find the number of ways in which this committee can be chosen if
(i) all are equally eligible,
(ii) the committee must consist of 1 woman and 2 men,
(iii) all are equally eligible except that any husband and wife cannot both serve in the committee.
CJC · Lecture · Example 9
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.