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One hundred tickets, numbered 1,2,3,...,100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip

One hundred tickets, numbered 1,2,3,...,100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if (a) If there are no restrictions? (b) the people holding tickets 19,47, and 73 all win prizes? (c) none of the people holding tickets 19,47,73, and 97 wins a prize? (d) the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes?

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