Financial Risk Manager Part 1

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