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# Pre-Cal 40S May 13, 2009

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Combinatorics workshop and introduction to Poker Combinations.

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### Pre-Cal 40S May 13, 2009

1. 1. How many ways can we divy this up? You ﬁgu out , I'm re it eati ng. Whose counting the E-Numbers boys by ﬂickr user law_keven
2. 2. Determine the indicated term in the expansion. The 4th term in the expansion of
3. 3. Determine the indicated term in the expansion. The middle term in the expansion of
4. 4. From a class of 12 boys and 10 girls a committee of 3 people is selected. How many different committees have at least one boy?
5. 5. From a class of 12 boys and 10 girls a committee of 3 people is selected. How many different committees have at least one boy?
6. 6. From a class of 12 boys and 10 girls a committee of 3 people is selected. How many different committees have at least one boy?
7. 7. 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.)
8. 8. 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?
9. 9. Poker Combinatorics or How likely is THAT?!? Red Hot Poker by ﬂickr user kimberlyfaye
10. 10. Poker Combinations 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]
11. 11. THE REST OF THESE QUESTIONS ARE HOMEWORK (b) Straight ﬂush [ﬁve cards in sequence and of the same suit, but not ace king queen jack ten]
12. 12. (c) Four of a kind [four cards of one face value and one other card]
13. 13. (d) Full house [3 cards of one face value and 2 cards of another face value]
14. 14. (e) Flush [5 cards of the same suit but not in sequence, not including the straight ﬂush and royal ﬂush above]
15. 15. (f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]
16. 16. (g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]
17. 17. (h) Two pairs [one pair of each two different face values and a card of a third face value]
18. 18. (i) One pair [two of one face value, and 3 cards of different face values, no matching the pair]
19. 19. (j) No pairs [5 different face values, not in sequence, not all cards in the same suit]