[Combinatorics]
Problem: Let $T=70$. Chef Selma is preparing a burrito menu. A burrito consists of: (1) a choice of chicken, beef, turkey, or no meat, (2) exactly one of three types of beans, (3) exactly one of two types of rice, and (4) exactly one of $K$ types of cheese. Compute the smallest value of $K$ such that Chef Selma can make at least $T$ different burrito varieties.

Solution: Using the Multiplication Principle, Chef Selma can make $4 \cdot 3 \cdot 2 \cdot K=24 K$ different burrito varieties. With $T=70$, the smallest integral value of $K$ such that $24 K \geq 70$ is $\left\lceil\frac{70}{24}\right\rceil=3$.

Final answer: 3