The number of possible orderings of a standard 52‑card deck is 52 factorial (52!), roughly 8.06 × 10^67, a number so enormous that it far exceeds common estimates for the number of atoms on Earth.
The math behind it
The total number of distinct arrangements for 52 unique cards is the factorial of 52, written 52!, which multiplies every integer from 1 to 52; evaluating that product yields a value on the order of 10^67, meaning each proper, thorough shuffle produces an ordering that is almost certainly unique in history.
Why it matters
This comparison illustrates how quickly factorial growth outpaces familiar large counts: while numbers like atoms, grains of sand, or stars sound unimaginably large, combinatorics with surprisingly small sets (52 items) produces far larger totals, which is why mathematicians and educators use the shuffled‑deck example to convey scale and probability.
Practical note
In practice, everyday shuffles rarely sample the entire permutation space uniformly, but even so the space is so huge that two independently shuffled full decks will almost always be in distinct orders; this fact is a fun reminder of how simple systems can hide enormous complexity and why chance can feel effectively limitless in many real‑world situations.