lucabrasi

Alright, times up, folks Here's how I did it:

The chances that all three pick a particular hotel:

(1/5)^3.

But there five hotels, so there chances that all three will pick the same hotel are:

5(1/5)^3.

The chances that two particular people will choose the same hotel and the third will choose a different hotel are:

(1/5)^2*(4/5).

But theres 3 combinations of two people and five hotels so the total chances of two being in the same and one being in another are:

3*5((1/5)^2*(4/5)).

In total, the chances that theyre at a different hotel are:

1-(1/5)^2*(4/5)-3*5((1/5)^2*(4/5)) = 0.48.

The more logical way to do it is:
The chances that the second person chooses a different hotel then the first = 4/5. The chances that the third chooses a different hotel then the first two = 3/5.

Chances that they all choose different hotel:

(4/5)(3/5) = 0.48.

My mind causes me to waste hours and hours of time