1. Let's solve a challenging factorial problem: Calculate $$\frac{10!}{8!}$$. 2. Recall the factorial definition: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 1$$. 3. Important rule: When dividing factorials like $$\frac{10!}{8!}$$, you can cancel the common terms. 4. Write out the factorials: $$10! = 10 \times 9 \times 8!$$ 5. Substitute into the expression: $$\frac{10!}{8!} = \frac{10 \times 9 \times 8!}{8!}$$ 6. Cancel $$8!$$ from numerator and denominator: $$= 10 \times 9$$ 7. Multiply the remaining terms: $$= 90$$ 8. Final answer: $$\frac{10!}{8!} = 90$$.