For a daily lottery, players pay $1 and pick any three-digit number. Then a number (between 000 and 999) is...

3. For a daily lottery, players pay $1 and pick any three-digit number. Then a number (between 000 and 999) is randomly selected. If a player's number is selected exactly, the player wins $500. If all three digits of the player's number are selected but in the wrong order (for example, 321 instead of 123), then the player wins $50.
(a) Find the expected gain when a player plays once and picks the number 789.
(b) Is this a fair game? Why or why not?
(c) Would it help if the player chose a different number like 267?