QQuestionPhysics
QuestionPhysics
Are there more ways to shuffle a deck of cards than there are atoms on Earth?
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Answer
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Step 1:: Understand the problem
We need to compare two very large numbers: the number of ways to shuffle a deck of cards and the number of atoms on Earth.
Step 2:: Calculate the number of ways to shuffle a deck of cards
52! \approx 8.06 \times 10^{67}
A standard deck has 52 cards. The number of permutations (or unique arrangements) of these cards is given by the factorial function: For a deck of 52 cards, this is:
Step 3:: Calculate the number of atoms on Earth
10^{50} mathrm{~kg} / (10^{-26} mathrm{~kg/atom}) \approx 10^{76}
The estimated number of atoms in the Earth's crust is around 10^51. However, this is much smaller than the total number of atoms in the Earth, which is estimated to be around 10^50 kg divided by the average atomic mass of about 10^- 26 kg:
Step 4:: Compare the two numbers
We have: - Number of shuffles: ~8.06 x 10^67 - Number of atoms on Earth: ~10^76 So, there are significantly more ways to shuffle a deck of cards than there are atoms on Earth.
Final Answer
Yes, there are more ways to shuffle a deck of cards than there are atoms on Earth.
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