8. (10 points) Three households, A, B, and C, plan to subscribe to newspapers. There are 5 different newspapers available. It is known that each household subscribes to two different newspapers, and any two households have exactly one newspaper in common. How many different subscription methods are there for the three households?
8. (10 points) Households A, B, and C plan to subscribe to newspapers, with 5 different newspapers available for selection. It is known that each household subscribes to two different newspapers, and it is also known that each pair of households subscribes to exactly one common newspaper. How many different subscription methods are there for the three households?
【Solution】Solution: From the problem, we know there are two different subscription types: $a b, a c, a d$ and $a b, a c, b c$: $a b, a c, a d$ has $\mathrm{C}_{5}^{1} \times \mathrm{A}_{4}^{3}=5 \times(4 \times 3 \times 2)=5 \times 24=120$ ways; $a b, a c, b c$ has $C_{5}^{3} \times C_{3}^{3}=10 \times 6=60$ ways.
Therefore, there are a total of $120+60=180$ different subscription methods.