$1 \cdot 90$ Given $n$ lines in a plane, where no two are parallel and no three are concurrent. How many intersection points do these lines have? How many triangles can these lines generate? How many parts does the plane get divided into by these lines? How many of these parts are unbounded?

Given $n$ lines in a plane, where no two are parallel and no three are concurrent:
- The number of intersection points is $\binom{n}{2} = \frac{n(n-1)}{2}$.
- The number of triangles generated is $\binom{n}{3} = \frac{n(n-1)(n-2)}{6}$.
- The number of parts the plane is divided into is $\frac{n(n+1)}{2} + 1$.
- The number of unbounded parts is $2n$.
［Solution］Since no two lines are parallel and no three lines are concurrent, each pair of lines has one intersection point, and each intersection point is the intersection of only these two lines. Therefore, the number of intersection points is equal to the number of pairs of lines, which is $C_{n}^{2}=\frac{1}{2} n(n-1)$.

From the given conditions, every three lines intersect to form a triangle, and this correspondence is one-to-one. Therefore, the total number of triangles is $C_{n}^{3}=\frac{1}{6} n(n-1)(n-2)$.

Next, we use the recursive method to calculate how many parts $n$ lines divide the plane into. Let $a_{k}$ be the number of parts that $k$ lines divide the plane into: the $(k+1)$-th line intersects with the previous $k$ lines at $k$ distinct points, and it is divided into $k+1$ segments by these $k$ points. Each segment splits the part it lies in into two parts. Therefore, we have
$$
a_{k+1}=a_{k}+k+1 .
$$

By this recursion, we get
$$
a_{n}=n+(n-1)+\cdots+2+a_{1}=\frac{1}{2} n(n+1)+1 .
$$

Finally, we note that each of the $n$ lines is divided into $n$ segments by the other $n-1$ lines, with exactly two of these segments being unbounded rays. Therefore, there are $2 n$ rays in total. Among the parts divided by the $n$ lines, the boundary of each unbounded region consists of exactly two rays, and each ray is the common boundary of two unbounded regions. Therefore, there are $2 n$ unbounded parts.