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# Pre-Cal 40S Slides November 30, 2007

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Poker probabilities and combinatorics.

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### Pre-Cal 40S Slides November 30, 2007

1. 1. Poker Probabilities ... I Win
2. 2. There are 10 football teams in a certain conference. How many games must be played if each team is to play every other team just once?
3. 3. There are 9 chairs in a row. In how many ways can 4 students be seated in consecutive chairs? (Hint: First find the number of ways of choosing 4 consecutive chairs.)
4. 4. Seven people reach a fork in a road. In how many ways can they continue their walk so that 4 go one way and 3 the other?
5. 5. Given a standard deck of 52 cards, how many ways are there to draw 5 cards to obtain each hand. (a) Royal Flush [ace, king, queen, jack, ten in the same suit] (b) Straight flush [five cards in sequence and of the same suit, but not ace king queen jack ten] (c) Four of a kind [four cards of one face value and one other card] The rest of this slide and those that follow is HOMEWORK. (d) Full house [3 cards of one face value and 2 cards of another face value]
6. 6. (e) Flush [5 cards of the same suit but not in sequence, not including the straight flush and royal flush above]
7. 7. (f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]
8. 8. (g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]
9. 9. (h) Two pairs [one pair of each two different face values and a card of a third face value]
10. 10. (i) One pair [two of one face value, and 3 cards of different face values, no matching the pair] (j) No pairs [5 different face values, not in sequence, not all cards in the same suit]