Playing a game at a large social event, Elaine pays $20 to claim three numbers from 1 through 20 without repetition. Near the end of the event, three different winning numbers will be drawn at random from 1 through 20. Elaine will receive $20 if she has exact one winning number, $50 if she has exact two winning numbers, $200 if she has three winning numbers, and nothing if there is no match.   (a) Find Elaine’s expected net gain and the standard deviation of her net gain.   (b) Assume that 300 people played this game at the event. Find the expected net gain of the event organizer from this game assuming there is $200 fixed cost.

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