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Thirty tickets, numbered 1,2, 3,..., 30, are sold to 30 different people for a drawing. Four different prizes are awarded, including a grand prize. How

Thirty tickets, numbered 1,2, 3,..., 30, are sold to 30 different people for a drawing. Four different prizes are awarded, including a grand prize. How many ways are there to award the prizes if

  1. the person holding ticket 27 wins one of the prizes?
  2. the people holding tickets 19 and 23 both win prizes?
  3. the people holding tickets 5, 19, 23, and 29 all win prizes?
  4. none of the people holding tickets 5, 19, 23, and 29 wins a prize?

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