2. Choose two elements from the set $\{1,2, \cdots, 11\}$ as $m$ and $n$ in the ellipse equation $\frac{x^{2}}{m^{2}}+\frac{y^{2}}{n^{2}}=1$. Then the number of ellipses that can be formed within the rectangular region
$$
B=\{(x, y)|| x|<11,| y \mid<9\}
$$

is ( ).
(A) 43
(B) 72
(C) 86
(D) 9
2. B.

According to the problem, $m$ is a positive integer not greater than 10, and $n$ is a positive integer not greater than 8. First, determine $n$, which has 8 possibilities; for each determined $n$, $m$ has $10-1=9$ possibilities. Therefore, the number of ellipses that satisfy the conditions is $8 \times 9=72$.