Question

Eight people are randomly sat at a round table. What is the probability the people are sitting in alphabetical order?

Answer 1

I believe these questions are solved by multiplying the amount of people by itself so the answer would be 1/64 because there 64 different combinations

Answer 2

For circular arrangements like a round table, it is difficult to say where the sequence of people would start from. So we will fix the position for the person who is first in alphabetical order. Then we will arrange remaining seven people.

Total number of ways to arrange seven people would be (7 x 6 x 5 x 4 x 3 x 2 x 1) = 5,040 ways.

And there will be only 1 arrangement when all people are in alphabetical order.

So probability would be
`(1)/(5,040) \;or\; 0.0198\%`