$\backslash$#$1$ From lecture, we know that the number of BST $($Binary search Tree$)$ shapes with $\backslash (\backslash$mathbf$\{3\}\backslash )$ nodes is $5.$

Suppose a student does not know this. The student draws all possible BSTs with $2$ nodes.

The student knows that there are $2$ possible BST shapes with two nodes. Each of the two BSTs above have $3$ null pointers. The root has $1$ and the leaf has $2$ null pointers. The student adds a $\backslash (3^\{\backslash$text $\{$rd $\}\}\backslash )$ node to each of the $3$ null pointers to each of the $2$ BST $($above$).$ The student concludes that there are $6$ possible shapes of a BST with $3$ nodes.

Briefly and clearly explain why the student's answer is wrong.