Let $T$ be a binary search tree with 15 nodes. The minimum and maximum possible heights of $T$ are: Note: The height of a tree with a single node is 0.

Given $N = 15$ nodes and the height of a single node tree is $0$:

1. Minimum Height ($h_{\min}$): The height is minimized when the tree is as balanced and full as possible. For height $h$, the maximum number of nodes in a binary tree is:

   $$N_{\max} = 2^{h+1} - 1$$

   For $N = 15$ nodes:

   $$15 \le 2^{h+1} - 1 \implies 2^{h+1} \ge 16 \implies h+1 \ge 4 \implies h_{\min} = 3$$

2. Maximum Height ($h_{\max}$): The height is maximized when the binary search tree is completely skewed (degenerate into a linked list).

   $$h_{\max} = N - 1 = 15 - 1 = 14$$

Therefore, the minimum and maximum possible heights are 3 and 14 respectively, corresponding to option (B).