Question

Here are 5 hotels in a certain town. if 3 people check into hotels in a day, what is the probability that they each check into a different hotel? what assumptions are you making?

Answer 1

There are 5 hotels. Each of these 3 people will have 5 ways to choose the hotel. By basic principle of counting, the total number of ways to which the hotels can be chosen is equal to ,
     5 x 5 x 5

That is, multiplying the number of ways each can choose the hotel. The answer is 125.

If each of them are to stay in different hotels, the first one will have 5 choices. The second will have only 4. Lastly, the third will only have 3 choices. That is,
     5 x 4 x 3 = 60

We divide the second answer by the total and multiply by 100% to get the probability.
    P = (60/125) x 100%
    P = 48%

ANSWER: 48%