Here is a way to model this. Say that there is a lady A and a man X.
There are different grouping of four for A to be in.
That is, there are thirty-five pairing of four for the ladies.
That same logic holds for groups of four men containing X.
Now pair each female group containing A with a male group containing X.
Then pair each female group containing A with a male group not containing X.
How many such pairing do you get?
Is that the answer?