Seated in order of age
Five friends of different ages sit down at random around a round table with five seats. Find the probability that, going around the table in one direction or the other, they are seated in increasing order of age.
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Fix the youngest person's seat; only the order of the others around the table matters.
How many orders of the other four are there, and how many of them work?
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Rotate the picture so that the youngest is in a fixed seat. Then the other four sit in one of equally likely orders going clockwise, and exactly two of these orders work.
Step 1. With the youngest fixed, reading clockwise, the other four appear in one of 24 equally likely orders.
Step 2. Increasing order of age clockwise is one of them; increasing order counterclockwise means decreasing order clockwise, which is another.
Step 3.