# Q. 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?

(a) 27

(b) 36

(c) 44

(d) 45

Correct Answer: (d) 45

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

# Raj has 10 pairs of red, 9 pairs of white, 8 pairs of black shoes.

In the worst-case scenario, Raj would pick one shoe from each pair without getting a matching pair.

There are ten pairs of red shoes, nine pairs of white shoes, and eight pairs of black shoes, which means there are a total of 27 pairs of shoes.

If he picks one shoe from each pair, that’s 27 attempts.

Then, he would have to start picking a second shoe from each pair. In the worst-case scenario, he would pick all the second shoes from the white and black pairs before picking a second shoe from a red pair.

That’s an additional 17 attempts (9 white pairs + 8 black pairs).

So, in total, the maximum number of attempts he would have to make is 27 (first shoes) + 17 (second shoes) = 44 attempts.

But, he still hasn’t picked a matching pair of red shoes. He would have to pick one more shoe (the matching red one) to get a pair.

So, the total maximum number of attempts is 44 + 1 = 45 attempts.

Hence, the correct answer is (d) 45.