Card combinatorics

Seeing this tweet earlier today made me think about combinatorics — in particular, combinations and permutations of the number of ways that a particular event can occur.

With a pack of 52 standard playing cards, the number of unique permutations is:

\begin{array}{lcl} 52! & = & 80658175170943878571660636856403766975289505440883277824000000000000 \\  & = & c.8.06 \times 10^{67} \end{array}

Which is a staggeringly big number — perhaps too big to truly comprehend; watch this excellent video to get an idea of the scale. But back to the sentiment of the tweet and thinking about collisions: given a specific shuffle ordering, has that ordering ever previously occurred? Extremely unlikely.

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