9 a. In a TV game show, there are 5 prizes behind 5 separate curtains. The...

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9 a. In a TV game show, there are 5 prizes behind 5 separate curtains. The show MC hands the contestants 5 cards with the names of each prize written on a different card. The contestant then places the cards in front of the curtains any way they choose. The curtains are then raised, and the contestant wins the prizes where there is a match. What is the probability that the contestant wins all 5 prizes? b. Professor Random plans to give a quiz by writing questions on small cards, one question per card. The set will consist of 7 calculus problems, 5 statistics problems, and 3 discrete math problems. A student draws 4 of these cards for his quiz. What is the probability that (a) all 4 of the problems will turn out to be statistics problems? (b) at least one of the problems will be a calculus problem? 9 a. In a TV game show, there are 5 prizes behind 5 separate curtains. The show MC hands the contestants 5 cards with the names of each prize written on a different card. The contestant then places the cards in front of the curtains any way they choose. The curtains are then raised, and the contestant wins the prizes where there is a match. What is the probability that the contestant wins all 5 prizes? b. Professor Random plans to give a quiz by writing questions on small cards, one question per card. The set will consist of 7 calculus problems, 5 statistics problems, and 3 discrete math problems. A student draws 4 of these cards for his quiz. What is the probability that (a) all 4 of the problems will turn out to be statistics problems? (b) at least one of the problems will be a calculus problem?