1. The problem asks to evaluate the combination expression $15C4$, which represents the number of ways to choose 4 items from 15 without regard to order. 2. The formula for combinations is: $$nCr = \frac{n!}{r!(n-r)!}$$ where $n$ is the total number of items, and $r$ is the number of items chosen. 3. Substitute $n=15$ and $r=4$: $$15C4 = \frac{15!}{4!(15-4)!} = \frac{15!}{4!11!}$$ 4. Simplify the factorial expression by expanding only the necessary terms: $$15C4 = \frac{15 \times 14 \times 13 \times 12 \times \cancel{11!}}{4! \times \cancel{11!}} = \frac{15 \times 14 \times 13 \times 12}{4!}$$ 5. Calculate the numerator: $$15 \times 14 = 210$$ $$210 \times 13 = 2730$$ $$2730 \times 12 = 32760$$ 6. Calculate the denominator: $$4! = 4 \times 3 \times 2 \times 1 = 24$$ 7. Divide numerator by denominator: $$15C4 = \frac{32760}{24}$$ 8. Simplify the fraction by canceling common factors: $$\frac{\cancel{32760}^{1365}}{\cancel{24}^{1}} = 1365$$ 9. Since the result is an integer, the value of $15C4$ is 1365. Final answer: $$15C4 = 1365$$