Question

What is the probability that 7 men who took their seats randomly at a round table are in alphabetical order? They can be in order either clockwise or counterclockwise.

Answer 1

1/360 ≈ 0.278%

Explanation:

First, find the total number of ways the men can be seated. When the first person sits, there are 6 possible men who can sit next to him. After that, there are 5 possible men who can sit next. So on and so forth. So the total number of ways is:

6×5×4×3×2×1 = 6! = 720

There are only 2 ways that the men can be arranged in alphabetical order: clockwise and counterclockwise. So the probability is:

P = 2 / 720

P = 1 / 360

P ≈ 0.278%