Question #8d994
2 Answers
We first choose one man and one woman, and then the third person. This will have no influence as there is no functional difference between the committee members.
Man:
Woman:
Third person:
Answer seems to be:
The third person is either a man or a woman, between which the order is not important, so we have to divide by
Real answer:
The (b)-question is ambiguous: does it mean: if they marry inside the group? Or if they marry at all?
(a) Consider the two separate possibilities:
and
If
and the selection of men in
5 ways
The combined number of ways of selecting 3 people of whom 2 are women can be done in
Similarly if
The two possibilities are mutually exclusive so the total number of ways of making the described selection is
(b) If only one couple is married (I assume intra-group marriage)
for the situation when 2 women are selected, there are
So the combined number of ways of selecting 3 people of whom 2 are women and the man is not married to either woman is
For the situation when 2 men are selected, there are
and the total number of ways of making the described selection (with no married couple selected) is
