Consider a binary tree $T$ in which every node has either zero or two children. Let $n > 0$ be the number of nodes in $T$. Which ONE of the following is the number of nodes in $T$ that have exactly two children?

Let $n_0$ be the number of leaf nodes (nodes with 0 children), $n_1$ be the number of nodes with 1 child, and $n_2$ be the number of nodes with 2 children.

For any binary tree:

Since every node in $T$ has either zero or two children, $n_1 = 0$. The total number of nodes $n$ is:

Substitute $n_0 = n_2 + 1$ into the total node equation:

Solving for $n_2$:

Thus, the number of nodes having exactly two children is $\frac{n-1}{2}$, which corresponds to (B).