1. The problem is to simplify the expression $15c5$. 2. Assuming $15c5$ represents a combination, it means the number of ways to choose 5 items from 15, denoted as $\binom{15}{5}$. 3. The formula for combinations is $$\binom{n}{r} = \frac{n!}{r!(n-r)!}$$ where $n=15$ and $r=5$. 4. Calculate factorials: $$15! = 15 \times 14 \times 13 \times 12 \times 11 \times 10!$$ but we can simplify without full factorials. 5. Simplify numerator and denominator: $$\binom{15}{5} = \frac{15 \times 14 \times 13 \times 12 \times 11}{5 \times 4 \times 3 \times 2 \times 1}$$ 6. Calculate numerator: $15 \times 14 = 210$, $210 \times 13 = 2730$, $2730 \times 12 = 32760$, $32760 \times 11 = 360360$. 7. Calculate denominator: $5 \times 4 = 20$, $20 \times 3 = 60$, $60 \times 2 = 120$, $120 \times 1 = 120$. 8. Divide numerator by denominator: $$\frac{360360}{120} = 3003$$. 9. Therefore, $15c5 = 3003$.