In 5.21(b) you want to do something similar as in part (a). This time you don't want to use the full set $S = \{1,2,3,4,5,6,7,8\}$, but the subset of odd numbers $\{1,3,5,7\}$.

For 5.24(c): Start by choosing which of the boxes will have exactly $2$ balls. Now, how many balls do you still have to place? In how many boxes? In how many ways can you place the remaining balls into the remaining boxes? Then use the product rule to find the answer.

In 5.30: Since you want $c + d = 3$ and $15 = 3 \times 5$, you want to find the number of solutions of the equation $a + b = 5$ and also $c + d = 3$. You can use stars and bars to find how many different solutions you can find to each equation, and then the product rule to combine your results to find the final answer.