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# Pre-Cal 40S Slides April 24, 2007

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More applications of permutations and combinations including a discussion of poker hand combinations.

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### Pre-Cal 40S Slides April 24, 2007

1. 1. There are 9 chairs in a row. In how many ways can 4 students be seated in consecutive chairs?
2. 2. Consider the digits 1, 3, 5, 7, 9. If repetitions are allowed, find: (a) how many 3 digit numbers can be formed. (b) How many 3 digit numbers can be formed if they must be less than 600 and divisable by 5.
3. 3. In how many ways can 8 books be arranged on a shelf if 3 particular books must be together?
4. 4. Given a standard deck of 52 cars, 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] (d) Full house [3 cards of one face value and 2 cards of another face value]
5. 5. (e) Flush [5 cards of the same suit but not in sequence, not including the straight flush and royal flush above]
6. 6. (f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]
7. 7. (g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]
8. 8. (h) Two pairs [one pair of each two different face values and a card of a third face value] .
9. 9. 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?
10. 10. 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?
11. 11. (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] HOMEWORK