Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
- A27
- B36
- C44
- D45Correct
Explanation
To find the maximum number of attempts, we must consider the worst-case scenario. This is the situation where Raj picks the maximum possible number of shoes without ever completing a red pair.
Step 1: Pick all non-red shoes. There are 9 pairs of white shoes (18 shoes) and 8 pairs of black shoes (16 shoes). 18 + 16 = 34 shoes.
Step 2: Pick red shoes without forming a pair. There are 10 pairs of red shoes (20 shoes). To avoid forming a pair, he could pick one shoe from each of the 10 red pairs. This adds 10 more shoes.
At this point, Raj has picked 34 + 10 = 44 shoes and still does not have a matching red pair.
Step 3: Pick the final shoe. The very next shoe he picks (the 45th attempt) must be the second shoe of one of the 10 red pairs he already started. This finally completes a red pair.
Therefore, the maximum number of attempts is 45. The correct option is D.
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