(5). (10 points) there are 5 hotels in stony brook. if 3 people check into hotels on september 12, what is the probability that they each check into a different hotel? (what assumptions are you making? ) make sure to define any notation you use to describe elements of the sample space.

0.48

Step-by-step explanation:

Probability that the first person chooses a hotel

⁵C₁

Probability that the second person chooses a different hotel

⁴C₁

because the choice of hotels has reduced by 1 as one hotel is occupied by the first person

Probability that the second person chooses a different hotel

³C₁

because the choice of hotels has reduced by 2 as two different hotels are occupied by the first person and second person

∴ The favorable outcomes are =⁵C₁×⁴C₁׳C₁=5×4×3=60

The total number of outcomes=5³=125

∴Probability that they each check into a different hotel=60/125=0.48

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