1. Two ordered pairs $(a, b)$ and $(c, d)$, where $a, b, c, d$ are real numbers, form a basis of the coordinate plane if $a d \neq b c$. Determine the number of ordered quadruples $(a, b, c, d)$ of integers between 1 and 3 inclusive for which $(a, b)$ and $(c, d)$ form a basis for the coordinate plane.
Answer: $\square$
Any pair of distinct points will form a basis except when $(a, b)$ and $(c, d)$ are both from $\{(1,1),(2,2),(3,3)\}$, so the answer is $9 \cdot 8-3 \cdot 2=66$.