9.11 In a confectionery shop, three types of pastries are sold: Napoleons, eclairs, and sponge cakes. In how many ways can you buy 9 pastries?
9.11 Here, we need to find the number of all possible combinations of 9 elements that can be formed from the given three elements, where these elements can repeat in each combination, and the combinations differ from each other by at least one element. This means we are looking for the number of combinations with repetitions of 3 elements taken 9 at a time. Using formula (9.5), we find

$$
\widetilde{C}_{3}^{9}=C_{11}^{9}=C_{11}^{2}=\frac{11 \cdot 10}{2}=55
$$

Answer: 55 ways.