Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks…
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?
27
36
44
45
Solution
There are 10 red pairs (20 red shoes: 10 left, 10 right), 9 white pairs (18 shoes) and 8 black pairs (16 shoes). In the worst case Raj picks all 18 white + 16 black = 34 non-red shoes, then picks all 10 red shoes of one foot (say all 10 left red shoes). That is 34 + 10 = 44 picks with no red pair yet. The 45th pick must be a right red shoe, completing a red pair. Maximum attempts = 45.