1. The problem is to evaluate the expression $$\frac{9!}{5!4!}$$. 2. Recall the factorial definition: $$n! = n \times (n-1) \times \cdots \times 1$$. 3. The expression resembles a binomial coefficient formula $$\binom{9}{4} = \frac{9!}{5!4!}$$ which counts combinations. 4. Calculate the factorials partially to simplify: $$\frac{9!}{5!4!} = \frac{9 \times 8 \times 7 \times 6 \times \cancel{5!}}{\cancel{5!} \times 4 \times 3 \times 2 \times 1}$$ 5. Cancel the common $5!$ terms: $$= \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$$ 6. Simplify the denominator: $$4 \times 3 \times 2 \times 1 = 24$$ 7. Calculate the numerator: $$9 \times 8 = 72, \quad 72 \times 7 = 504, \quad 504 \times 6 = 3024$$ 8. Divide numerator by denominator: $$\frac{3024}{24} = 126$$ 9. Therefore, the value of the expression is $$126$$.