Maximum attempts to draw a red pair of shoes

To determine the maximum number of attempts (the absolute worst-case scenario), we must assume Raj draws every single non-red shoe, and then draws single mismatched red shoes before completing a pair .

Convert shoe pairs into individual units: Red shoes = 10 × 2 = 20 units . White shoes = 9 × 2 = 18 units . Black shoes = 8 × 2 = 16 units.

Step 1: Draw all non-red shoes first to maximize failure: Total non-red = 18 (white) + 16 (black) = 34 attempts.

Step 2: Draw red shoes. To delay forming a pair, Raj could draw 10 shoes that all belong to the same foot orientation (e.g., 10 left red shoes) . Attempts added = 10.

Step 3: The very next shoe drawn (34 + 10 + 1 = 45th attempt) is guaranteed to be a right red shoe, completing a matching functional pair . Total maximum attempts = 34 + 10 + 1 = 45.

Answer: (d).