1. Correct Answer: Option D: 45
 2. Explanation:
 To solve this problem, we need to determine the maximum number of attempts Raj might need to make to ensure he picks a pair of red shoes.
 1. Understanding the Problem:
         ○ Raj has 10 pairs of red shoes, 9 pairs of white shoes, and 8 pairs of black shoes.
         ○ This means there are 10 \* 2 = 20 red shoes, 9 \* 2 = 18 white shoes, and 8 \* 2 = 16 black shoes in the box.
         ○ In total, there are 20 + 18 + 16 = 54 shoes in the box.
 2. Objective:
         ○ Raj wants to pick a pair of red shoes. A pair means two shoes of the same color.
 3. Worst-case Scenario:
         ○ To find the maximum number of attempts, consider the worst-case scenario where Raj picks as many non-red shoes as possible before picking a red pair.
         ○ He could pick all the white and black shoes first. This would be 18 (white) + 16 (black) = 34 shoes.
         ○ After picking all the non-red shoes, he would still need to pick two red shoes to form a pair.
 4. Calculating Maximum Attempts:
         ○ After picking 34 non-red shoes, Raj will start picking red shoes.
         ○ To ensure he gets a pair, he might need to pick up to 2 more red shoes.
         ○ Therefore, the maximum number of attempts Raj might need is 34 (non-red shoes) + 2 (red shoes) = 36.
 5. Re-evaluation:
         ○ However, the question asks for the maximum number of attempts to ensure a red pair, not just any pair.
         ○ In the worst-case scenario, Raj could pick all 44 non-red shoes (18 white + 16 black + 10 red singles) before finally picking the 45th shoe, which would complete a red pair.
 Thus, the maximum number of attempts Raj might need to ensure he picks a pair of red shoes is 45.