WMC 2018 Senior Problem 2

Level 1

A hotel shuttle picks up 3 passengers at an airport and stops at 4 different hotels. What is the probability the 3 passengers are staying at 3 different hotels?

3 8 \frac { 3 }{ 8 } 2 9 \frac { 2 }{ 9 } 1 3 \frac { 1 }{ 3 } 1 2 \frac { 1 }{ 2 } None of these

Tiger Ang by Tiger Ang , 20, Malaysia

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1 solution

Julian Yu
Oct 10, 2018

The number of ways the three people can stay in three different hotels is 4 ⋅ 3 ⋅ 2 = 24 4\cdot3\cdot2=24 . The number of ways they can stay in hotels without restrictions is 4 3 = 64 4^3=64 . Therefore, the probability is 24 64 = 3 8 \frac{24}{64}=\frac{3}{8} .

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