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

Answer:

1/360 ≈ 0.278%

Step-by-step 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%