Answer: 1260

## Explanation This is a **multinomial coefficient** problem where we need to arrange 9 stocks into three distinct categories with specific counts: - 4 small-cap stocks - 3 blue-chip stocks - 2 emerging market stocks ### Step 1: Total arrangements without considering categories If all 9 stocks were distinct, the total number of arrangements would be: $$9! = 362,880$$ ### Step 2: Accounting for identical categories However, within each category, the stocks are considered identical for labeling purposes. We need to divide by the factorial of the counts in each category: $$\text{Number of ways} = \frac{9!}{4! \cdot 3! \cdot 2!}$$ ### Step 3: Calculation $$\frac{9!}{4! \cdot 3! \cdot 2!} = \frac{362,880}{24 \cdot 6 \cdot 2} = \frac{362,880}{288} = 1,260$$ ### Step 4: Verification This represents the number of distinct ways to arrange 9 items where 4 are of one type, 3 are of another type, and 2 are of a third type. **Therefore, the correct answer is A. 1260**

Author: Tanishq Prabhu