This question already has an answer here:
I am doing a research paper about this topic. It has really puzzled me and although I seem to have found a way to calculate it, my answers are rather weird.
I assumed that since 1300 AD a total of approximately 1.546×10^20 times a set of cards have been shuffled (700 years x every second since then).
The probability that such permutation has never been seen before is then (1- 1/52!)^(1.546×10^20 ) and that it did happen is the answer - 1.
However, I always got the answer being equal to 1.
What am I missing? Any more tips and tricks concerning this topic, PLEASE do. I need to cover 12 pages.
Also: how long would it take until the chances increase of us seeing a permutation ever again?