1. The problem statement, all variables and given/known data 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? I realize that there are n choose k sets of k seats to be occupied, and that there are n-k+1 sets of k adjacent seats. So the probability that I'm looking for is: (n-k+1)/(n choose k) What I don't understand is how the above probability simplifies to: [(n-k+1)!k!]/n! Can someone please explain? Thanks. 2. Relevant equations (nk) = n choose k = n!/[(n-k)!k!] 3. The attempt at a solution (n-k+1)/(n choose k) = [(n-k+1)(n-k)!k!]/n! Not sure what to do from here.