Math 104 Exam 2
If you match 3 of the 5 powerball numbers, how much do you win?
$100
P(one pair)
1,098,240/52 choose 5
How many ways can I select a 4 person committee from a 10 person group?
10 choose 4 ways
Express P(10,3) as a quotient of factorials
10!/7!
P(straight)
10,200/52 choose 5
P(2 pair)
123,552/52 choose 5
Three of a kind
3 cards of the same rank Ex: J hearts, J clubs, J diamonds, 2 spades, 3 clubs
Full house
3 of one kind, 2 of another (rank) Ex: KKK 22
P(full house)
3,744/52 choose 5
How many numbers are in a craps game?
36
P(straight flush)
36/52 choose 5
P(royal flush)
4/52 choose 5
What does 4! mean?
4x3x2x1
Flush
5 cards of the same suit Ex: Ace of hearts, 3 of hearts, 7 of hearts, jack of hearts, 9 of hearts
Straight
5 consecutive cards Ex: 3 hearts, 4 clubs, 5 clubs, 6 diamonds, 7 spades
Straight flush
5 consecutive cards all in one suit Ex: 3,4,5,6,7 of hearts, clubs, spades, diamonds
P(flush)
5,108/52 choose 5
P(three of a kind)
54,912/52 choose 5
P(4 of a kind)
624/52 choose 5
P(6,3)
6x5x4
2 pair
A pair of one rank, and a pair of another rank Ex: J hearts, J clubs, and Ace of diamonds, Ace of spades, and 3 clubs
One pair
A pair of one rank, with 3 unrelated cards Ex: 5 clubs, 5 diamonds, 3 spades, ace of spades, Q hearts
What are the rules of craps?
Bets on shooters next roll. If the shooter rolls a sum of 2,3, or 12, then the bystander wins 3$ on a 1$ bet. If the shooter rolls an 11, then the bystander wins 7$. If the shooter rolls anything else, then the bystander loses.
What is the big red bet in craps?
Bystander bets on the next roll. If the person rolls a sum of 7, then the bystander wins $4 on a dollar bet. Otherwise the bystander loses.
8C4
C(8,4) = 8!/(8-4)4! = 70
Rules of Blackjack
Dealer deals every person 2 cards. Goal is to get as close to 21 without going over (busting). The dealer must hit themselves if less than or equal to 16 card value. If your cards add to 21 on first try, you say blackjack.
Card values of blackjack
Every card has a numberical value, a numbered card has that number. Ace has value of 1 or 11 and a KGJ or 10 has a value of 10.
Rules of texas holdem
Everybody is dealt 2 cards. Three common cards are dealt to the table (called the flop). One more common card is dealt (The turn). The final common card is dealt (the river)
The push in blackjack
If after all the dealing is done and your total is less than or equal to 21, and equal to the dealers, no money changes hands
Insurance bet in blackjack
If the dealer has an ace showing, then you can but are not required to place an insurance bet that if the dealer has a blackjack, you will win the bet. You win 2 dollars plus your original dollar back
Royal flush
KQJ10A of hearts, diamonds, clubs, or spades
Permutations
Order counts
Rules of powerball
Select 5 numbers between 1-69. Select a powerball number from 1-26. To win grand prize, you have to match all 5 numbers (order does not matter)
4 of a kind
four cards of the same rank, with any 5th card at all Ex: K,K,K,K,3
nPr
n!/(n-r)!
nCr
n!/(n-r)! r!
Combination formula (n/k)
n!/k!(n-k)!
Permutation formula and example
n!/n-k! P(6,3) = 6x5x4 = 6x5x4x3x2x1/3x2x1 = 6!/3!
Combinations
order doesn't matter
