playing cards

[skilliyay]

I think that if I was to shuffle a standard deck of 52 playing cards, that a deck of cards would never have been in that exact order anywhere in the world ever!
Do people agree or disagree?

[sarumite]

I imagine there must be several million possible combinations, but my maths isn't up to supplying the answer.
Where's crofter .. I feel sure he could offer a definitive solution!!??

[Quizmonkey]

Yes, but it's still a finite number - so, given how long so many people have been playing cards throughout the world, I would have thought every permutation would have been hit by now. Bit impossible to prove though...

[JerryB]

More than several million, I think, sarumite.
It's the total number of permutations of 52 distinct cards, which is 52! (aka 52 factorial, ie.,
52 x 51 x 50 x 49 x .......... x 2 x 1), which is
(deep breath)

80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

according to http://www.bjstrat.net/shuffles.htm

My calculator puts 52! as just over 8 x 10^67

[Quizmonkey]

Blimey!

[JerryB]

Or, to put it another way (roughly) -

if you assume a time of 5 seconds to shuffle a deck of cards, that's
12 shuffles a minute
= 720 shuffles an hour
= 17,280 shuffles a day (24 hours)
= 120,960 shuffles a week (7 days)
= 6,289,920 shuffles a year (52 weeks)

If you further assume 6.6 (American) billion people in the world, and EACH of them shuffling a deck, and producing UNIQUE results every time, that's

41,513,472,000,000,000 unique permutations a year.

And you'd still need
19,429,397,563,023,367,106,384,317,085,404,000,000,000,000,000,000 (1.94 x 10^51) years to get every permutation.

[Quizmonkey]

Don't get that last bit - your number of years is way higher than the number of permutations.