My Scando-Germanic friend, Odd Zahlen, often brings a die to class to answer multiple-choice final exam questions. Each multiple-choice question on this particular examination consists of three choices, and Odd decides to pick answer (a) if a 1 or 2 appears on a roll of the die, to pick (b) if a 3 or 4 appears on the die, or to pick (c) if a 5 or 6 appears. Assume that the correct answers are uniformly distributed among the choices (a), (b), and (c). What is the probability of obtaining exactly 5 correct answers on a ten question examination using this method?