Part A Poker Hands: In this activity, we will apply some of the various counting techniques that we have studied including the product and sum rules, the principle of inclusionexclusion, permutations, and combinations. Our application will be counting the number of ways to be dealt various hands in poker, and analyzing the results.
First, if you are not familiar with poker the following is some basic information. These are the possible 5card hands:
Royal Flush (A,K,Q,J,10 of the same suit);
Straight Flush (all 5 cards in order and the same suit);
Flush (same suit);
Straight (all 5 cards in order);
1 Pair;
2 Pair;
3ofaKind;
4ofaKind;
Full House (3ofakind and a pair);
Nothing (none of the above hands).
We will assume to be using a standard deck containing 52 cards: 4 suits (hearts, clubs, diamonds, and spades) each with the denominations A, K, Q, J, 10,…, 2 with four cards removed: 4 of hearts, 8 of spades, 3 of diamonds, and Jack of clubs. For this game, suppose that you are randomly dealt a 5card hand from the modified deck.
1. Count the number of
different ways to get each poker hand in your 48 card deck. The
order that you receive the cards does not matter. Show all
calculations used to obtain your answers. Do your best to arrive at
your answers using counting techniques such as combinations. (Note:
if you are unfamiliar with the game you could study the
calculations found in many resources on the web before attempting
to do these calculations on the modified deck.)
Hand 
Counts (48 card deck) 
Royal Flush 

Straight Flush 

Flush 

Straight 

1 Pair 

2 Pair 

3ofaKind 

4ofaKind 

Full House 

Nothing 
Get Answers For Free
Most questions answered within 1 hours.