Player A, picks $n_1$ integers $a_1$,...,$a_{n_1}$ uniformly at random from $1$..$N$,
and player B picks $n_2$ integers $b_1$,...,$b_{n_2}$ the same way.
Given $N$, $n_1$, $n_2$, and $d$, what is the expected number of pairs ($a_i$,$b_j$) where |$a_i$-$b_j$| $=<$ $d$,
A. if A and B are allowed to select duplicates in their lists.
B. if duplicate numbers are not allowed.
Thanks, MG