1. **Stating the problem:** We want to find the number of ways to choose 5 candies from 4 flavours: orange, grape, lemon, and mint. This is a problem of combinations with repetition. 2. **Formula used:** The number of ways to choose $k$ items from $n$ types with repetition allowed is given by the stars and bars theorem: $$\binom{n+k-1}{k}$$ 3. **Applying the formula for candies:** Here, $n=4$ (flavours) and $k=5$ (candies). $$\binom{4+5-1}{5} = \binom{8}{5}$$ 4. **Calculating $\binom{8}{5}$:** $$\binom{8}{5} = \frac{8!}{5!\times 3!} = \frac{8\times7\times6}{3\times2\times1} = 56$$ 5. **Answer for candies:** There are 56 ways to choose 5 candies from 4 flavours. --- 6. **Stating the second problem:** We want to find the number of ways to select 4 sandwiches from 5 fillings: tuna, chicken, egg, cheese, and ham, again with repetition allowed. 7. **Applying the formula for sandwiches:** Here, $n=5$ (fillings) and $k=4$ (sandwiches). $$\binom{5+4-1}{4} = \binom{8}{4}$$ 8. **Calculating $\binom{8}{4}$:** $$\binom{8}{4} = \frac{8!}{4!\times 4!} = \frac{8\times7\times6\times5}{4\times3\times2\times1} = 70$$ 9. **Answer for sandwiches:** There are 70 ways to select 4 sandwiches from 5 fillings. **Final answers:** - Candies: 56 ways - Sandwiches: 70 ways