- #1

EnzoF61

- 14

- 0

## Homework Statement

If k people are seated in a random manner in a circle containing n chairs (n>k), what is the probability that the people will occupy k adjacent chairs in the circle?

## The Attempt at a Solution

1) The total probability of k people seated in a circle of n chairs is [ (n "choose" k) = p1 ]

2) The amount of people occupying k adjacent chairs. We have (n-k) total unoccupied chairs. For a small chunk of the total number, (Kth Person, 1st Person, 2nd Person are all seated next to each other) or (2nd Person, 1st Person, Kth Person seated adjacently). => (n-k+2)=p2 total ways to seat adjacently (considering the two identical orders).

3) Solution = p2*p1 = (n-k+2) / (n "choose" k)