The answer is 350/27, but I don't know to get to it.

You want to open a casino with a new card game. In the game, a dealer will shufe a (full) deck of (standard) cards so they are fully-shufed (i.e. every ordering is equally likely). The dealer then ips over the top three cards. To play, a player pays $5. - If all three cards are diamonds, the player gets a payout of $20 ' If two cards are diamonds, the player gets a payout of $15 - If none of the cards are diamonds, the player gets no payout. You want all the games in your casino to be fair games the expected profit (payout minus cost) of your game should be $0. What should the payout be if exactly one of the cards is a diamond? Give your answer as a simplified fraction (don't worry if your number couldn't be paid out with standard US. currency)