Ten points are selected on the positive $x$-axis,$X^+$, and five points are selected on the positive $y$-axis,$Y^+$. The fifty segments connecting the ten points on $X^+$ to the five points on $Y^+$ are drawn. What is the maximum possible number of points of intersection of these fifty segments that could lie in the interior of the first quadrant?
$\text{(A) } 250\quad \text{(B) } 450\quad \text{(C) } 500\quad \text{(D) } 1250\quad \text{(E) } 2500$
$\fbox{B}$ We can pick any two points on the $x$-axis and any two points on the $y$-axis to form a quadrilateral, and the intersection of its diagonals will thus definitely be inside the first quadrant. Hence the answer is $10C2 \times 5C2 = 450$.