A car is parked among N cars standing in a row, but not at either end. On his return, the owner finds that exactly ''r'' of the N places are still occupied. The probability that the places neighboring his car are empty is

A car is parked by an owner amongst 25 cars in a row, not at either end. On his return he finds that exactly 15 places are still occupied. The probability that both the neighboring places are empty is

a. A rail road flat car of mass M can roll without friction along a straight horizontal track . Initially, a man of mass m is standing on the car which is moving to the right with speed v_(0) . What is the change in velocity of the car if the man runs to the left so that his speed relative to the car is v_(rel) just before he jumps off at the left end? b. If there are n men each of mass m on the car, should they all run and jump off together or should they run and jump one by one in order to give a greater velocity to the car?