If $k$ people are seated in a random manner in a row containing $n$ seats ($n > k$), what is the probability that the people will occupy $k$ adjacent seats in the row?
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?
For the first question, my solution is $\frac{(n-k+1)!k!}{n!}$. Is this correct? The solution to the second question is similar, but how do I take into account the circle instead of a line?