Want opinions on my approach to solving this problem

Question

Given any four non co-planar points in a $3-D$ space, find the number of triangular prisms that can be made.A triangular prism has 2 opposite faces as congruent triangles and the other three faces as parallelograms

Now I just want to check if my approach to this problem is correct.

Since the four points are non co-planar, we can pick any three and define a plane that contains these points. Now we just replicate the triangle formed by these three points about the 4th point and we have a triangular prism. I think we can make 4 of these.

Answer 1

You are correct. You can form a total of $C(4,3)=\frac{4!}{3!(4-3)!}=4$ triangular prisms with 4 points.