ChatGPT: How many possible combinations are there for a deck of 52 cards?
- Thread starter Goldhedge
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Highlights thread as a discussion with ChatGPT
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There are 52! (52 factorial) possible combinations for a deck of 52 cards. This is because each card can be arranged in any of the 52 slots available in the deck. The formula for calculating factorial is n! = n x (n-1) x (n-2) x ... x 1, where n is the number of items being arranged. So, for a deck of 52 cards, the calculation is:
52! = 52 x 51 x 50 x ... x 1
This results in a very large number, approximately 8.06 x 10^67, which is why it's often easier to use scientific notation to represent it.
52! = 52 x 51 x 50 x ... x 1
This results in a very large number, approximately 8.06 x 10^67, which is why it's often easier to use scientific notation to represent it.
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Compare this very large number to the number of stars in the known Universe...
The number of stars in the known universe is estimated to be around 10^22, which is much smaller than the number of possible combinations for a deck of 52 cards, which is approximately 8.06 x 10^67. This means that there are many more possible combinations of a deck of 52 cards than there are stars in the universe.
To put this in perspective, if there were as many stars in the universe as there are possible combinations for a deck of 52 cards, there would be enough stars to fill 1.5 billion Milky Way galaxies! It's a staggering difference, and it gives an idea of just how large the number of possible arrangements for a deck of cards is.