Short Answer 
The number of ways to shuffle a deck of cards (52!), which is approximately 8.0658 x 10^67, greatly exceeds the estimated 1.33 x 10^50 atoms on Earth. This comparison illustrates the vast diversity of card arrangements in relation to the finite quantity of atoms available on the planet.
Step 1: Understanding Card Shuffling
The number of possible ways to shuffle a deck of cards, denoted as 52!, represents the factorial of 52. This means you calculate it by multiplying all positive integers from 1 to 52. For example:
- 1 x 2 x 3 x … x 52
- This results in approximately 8.0658 x 10^67 unique arrangements of the cards.
Step 2: Estimating Atoms on Earth
Estimating the number of atoms on Earth is a complex task due to its vastness. Nevertheless, a commonly referenced figure is about 1.33 x 10^50 atoms. This estimate accounts for various components, such as:
- Atoms in the Earth’s crust
- Atoms in the oceans
- Atoms in the atmosphere
- Atoms in living organisms
Step 3: Comparing the Numbers
Upon comparing the two figures, it becomes clear that the number of ways to shuffle a deck of cards (52!) is significantly larger than the estimated number of atoms on Earth (1.33 x 10^50). Therefore, we can conclude that:
- The possibilities for card arrangements vastly outnumber the estimated atoms.
- This highlights the immense diversity of shuffles compared to the finite number of atoms on our planet.