1. **State the problem:** We want to find the number of ways to select 6 questions out of 10. 2. **Formula used:** The number of ways to choose $k$ items from $n$ items without regard to order is given by the combination formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. **Apply the formula:** Here, $n=10$ and $k=6$, so: $$\binom{10}{6} = \frac{10!}{6!(10-6)!} = \frac{10!}{6!4!}$$ 4. **Simplify factorials:** $$10! = 10 \times 9 \times 8 \times 7 \times 6!$$ So, $$\binom{10}{6} = \frac{10 \times 9 \times 8 \times 7 \times \cancel{6!}}{6! \times 4!} = \frac{10 \times 9 \times 8 \times 7}{4!}$$ 5. **Calculate $4!$:** $$4! = 4 \times 3 \times 2 \times 1 = 24$$ 6. **Evaluate numerator:** $$10 \times 9 = 90$$ $$90 \times 8 = 720$$ $$720 \times 7 = 5040$$ 7. **Divide numerator by denominator:** $$\frac{5040}{24} = 210$$ **Final answer:** There are $210$ ways to select 6 questions out of 10.