Poker probabilities and combinatorics.

1. Poker Probabilities ...
I Win

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?

4. 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.)

5. 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?

6. 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]

7. (e) Flush
[5 cards of the same suit but not in sequence, not including the
straight flush and royal flush above]

8. (f) Straight
[5 cards in sequence, but not all of same suit. Ace high or low]

9. (g) Three of a Kind
[exactly 3 cards of one face value and 2 different cards]

10. (h) Two pairs
[one pair of each two different face values and a card of a third face value]

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]