1. The problem is to generate 60 choose questions, which typically involve combinations. 2. The formula for combinations is given by $$C(n, k) = \frac{n!}{k!(n-k)!}$$ where $n$ is the total number of items and $k$ is the number of items chosen. 3. Important rules: - Order does not matter in combinations. - Factorials ($n!$) represent the product of all positive integers up to $n$. 4. Example question: "How many ways can you choose 3 students from a group of 10?" 5. Solution: $$C(10, 3) = \frac{10!}{3!\times 7!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120$$ 6. Another example: "How many ways to choose 5 books from 12?" 7. Solution: $$C(12, 5) = \frac{12!}{5!\times 7!} = \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1} = 792$$ These examples illustrate how to create choose questions and solve them using the combination formula.