In the daily lottery game "Guess 3," three different numbers are picked randomly from the numbers 0, 1,..., 9. The numbers are picked in order. To play this game, you must choose between "Exact order" and "Any order" on the entry form. In either case, the game costs $1 to play. Should you choose to play "Exact order," you must tick three different numbers in the order you think they will be picked. If those numbers are picked in that order, you win a $360 payoff. Should you opt to play "Any order," you tick three numbers without regard for their order of arrangement. You win a $160 payoff if those three numbers are picked. Set up a probability model to calculate the expected value of the payoff amount for both options.