For 25, as Derek mentions, it is similar to example 4.10. Consider three sets, where you count the number of ways friend 1, friend 2, and friend 3 get no books. Use them to find the number of ways at least one of the friends gets no books. Then use complementary counting.

For 26, try using complementary counting: how many regions would you have in a Venn diagram with three sets like the one described in the problem? Use this to find the total number of ways you could choose the sets $A$, $B$ and $C$. Then do the same assuming you only have two sets, this should help counting what happens when $A=\varnothing$.

On 30, when asked to do PIE consider sets where one of the friends gets no books (like in 25). To count using cases it might help figuring out first the different ways to add to $5$ using three positive numbers.