A set of 200 people consisting of 100 men and 100 women is randomly divided into 100 pairs of 2 each.

Number the men arbitrarily from 1 to 100, and for = 1,2,...100, let

Then X, the number of man-woman pairs, can be expressed as

Because man i is equally likely to be paired with any of the other 199 people, of which 100 are women, we have

Similarly, for i not equal to j,

what about variance?

why and ??