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# Pre-Cal 40S May 14, 2009

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Pre-Test and "counting" the number of different poker hands.

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### Pre-Cal 40S May 14, 2009

1. 1. How many of each hand are there in a deck? Poker Combinations and our pre-test I Win by ﬂickr user Kevin Labianco
2. 2. (5) In a 52 card deck, how many 5 card poker hands are possible that have exactly two pair? one pair?
3. 3. 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]
4. 4. (b) Straight ﬂush [ﬁve cards in sequence and of the same suit, but not ace king queen jack ten]
5. 5. (c) Four of a kind [four cards of one face value and one other card]
6. 6. (d) Full house [3 cards of one face value and 2 cards of another face value]
7. 7. (e) Flush [5 cards of the same suit but not in sequence, not including the straight ﬂush and royal ﬂush above]
8. 8. (f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]
9. 9. (g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]
10. 10. (h) Two pairs [one pair of each two different face values and a card of a third face value]
11. 11. (i) One pair [two of one face value, and 3 cards of different face values, no matching the pair]
12. 12. (j) No pairs [5 different face values, not in sequence, not all cards in the same suit]
13. 13. How many different necklaces of 12 beads each can be made from 18 beads of different colours? EXTRA PRACTICE ENJOY!
14. 14. (a) The last part of your telephone number contains four digits. How many such four-digit numbers are there? b) How many such four-digit numbers are there if the same digit cannot be used twice? c) How many four-digit numbers begin with a 2 ,4 or 0 if the same digit cannot be used twice?
15. 15. In how many ways can the student council choose a subcommittee of 5 people from the entire council which consists of 11 people?
16. 16. (a) How many 3-digit numbers can be formed if no digit is used more than twice in the same number? (b) How many of these numbers are odd? (c) How many of these numbers are divisable by 5?
17. 17. (a) How many different 4 digit numbers are there in which all the digits are different? (b) How many of these numbers are odd? (c) How many of these numbers are divisable by 5?
18. 18. A 120-room hotel has reservations from 6 guests for 6 different rooms. In how many ways can the rooms be assigned?
19. 19. How many ways can the batting order of a 9-member softball team be listed?
20. 20. A nickel and a quarter and a dime are tossed on a table. Create a tree diagram to determine how many ways these coins can land on the table. (The order in which the coins land doesn't matter; it will next week.)