A vague appointment Four people make an appointment to meet

A vague appointment: Four people make an appointment to meet each other at the café in town. However, this particular town has four cafés. What is the probability that none of them meet?

Solution

There are 4^4 = 256 ways to go to the 4 cafes.

Meanwhile, there are 4! = 24 ways to permute them, so that no 2 people are on the same cafe.

Thus,

P(none meets) = 24/256 = 0.09375 [answer]