# Answer e the total number of ways to assign truth

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Answer:____________________ (e) The total number of ways to assign truth values to five true-false problems with at least 2 of the answers being true is given by 5 C(5,k). k=2 Answer:____________________

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TEST2/MAD2104 Page 2 of 4 _________________________________________________________________ 3. (25 pts.) A standard deck of playing cards consists of 52 cards divided into 4 suits of 13 cards each. There are 2 black suits, spades and clubs, and there are 2 red suits, hearts and diamonds. Each suit consists of 10 spot cards ranging from 1 or ace through 10, and 3 face cards: jack, queen, and king. A hand in draw poker consists of 5 cards. For each of the following questions, either provide an appropriate integer or indicate unambiguously how your answer would be computed or explain why the given assertion is true. [Correct notation involving combinations or permutations may be used.] (a) How many draw poker hands are there? n = (b) How many ways can Frodo arrange the cards in his draw poker hand?? n = (c) How many draw poker hands have exactly 3 cards of one kind, e.g., 3 kings, or 3 aces, or 3 fives, and two other cards that are different from the three that are alike?? n = (d) Every draw poker hand has at least two cards of the same suit. Why? What magic principle applies here?? (e) Suppose the deck is well shuffled, so we may safely assume that the cards are randomly ordered. How many cards must Frodo be dealt from the top of the deck to ensure that he has 7 cards from the same suit.
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• Fall '08
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• Logic, pts, Natural number, induction step

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