7.48 $n$ planes passing through a certain point can divide the space into at most how many regions?
[Solution] Let $M_{0}, M_{1}, \cdots, M_{n-1}$ be planes passing through a fixed point $A$.
Construct a plane $N \parallel M_{0}$. Since the planes $M_{1}, M_{2}, \cdots, M_{n-1}$ all intersect with $M_{0}$, they also intersect with $N$, cutting off $n-1$ lines on $N$. These $n-1$ lines divide the plane $N$ into at most
$$
1+1+2+\cdots+(n-1)=1+\frac{n(n-1)}{2} .
$$

regions. Cones with vertex $A$ and these regions as bases, if their generatrices are extended infinitely, will divide the space into
$$
2 \times\left[1+\frac{n(n-1)}{2}\right]=2+n(n-1)
$$

regions. Half of these regions are above $M_{0}$, and the other half are below $M_{0}$.