Canasta is played with two decks of 52 cards each plus the 4 jokers. A standard Canasta hand consists of 11 cards. How many hands are possible?
so you want 11 of the 108 cards, which would be
C(108,11)
= appr 3.4 x 10^14
quite a few i would say
C(54,11) are duplicates
what about duplicate cards? There are two of each card, and 4 jokers.
Thanks Steve, you are right, I missed the duplications
I was thinking something along the lines of dividing by 2^52 , since we have pairs 52 times.
I don't know enough about jokers. Are the all the same or distinct?
I did count them in my 108 = 2x52+4
If they are the same, we have to divide by another 4!
To find out the number of possible hands in Canasta, we need to consider the total number of cards in the two decks (52 cards each), along with the 4 jokers.
First, let's calculate the total number of cards:
2 decks of 52 cards = 2 * 52 = 104 cards
Since we have 4 jokers as well, the total number of cards becomes:
104 + 4 = 108 cards
Next, we need to calculate the number of ways we can choose 11 cards out of the total 108 cards. This is represented by the combination formula, denoted as C(n, r), where n is the total number of cards and r is the number of cards in a hand.
Using the combination formula, the number of possible hands is calculated as follows:
C(108, 11) = (108!)/(11!(108-11)!)
= (108!)/(11! * 97!)
Now, calculating this mathematically would be quite tedious. However, there are calculators and software programs that can handle complex calculations like this. You can use a scientific calculator, an online combination calculator, or even programming languages like Python or R to calculate the result.
For example, using Python programming language and the math library, you can calculate the number of possible hands in Canasta using the following code:
```python
import math
total_cards = 108
cards_in_hand = 11
number_of_hands = math.comb(total_cards, cards_in_hand)
print("Number of possible hands in Canasta:", number_of_hands)
```
Once you run this code, it will give you the exact number of possible hands in Canasta.