What are the number of combinations that a deck of 52 playing cards
can be put into.  I understand you multiply 52*51*50*49 etc.  How
might you explain this very large number in sciencetif terms and
layman terms.  And what would the exact number look like & how would
you say it.  Thank You very much.

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Request for Question Clarification by pinkfreud-ga on 23 Sep 2004 21:38 PDT

I've found an excellent page that is aimed at the layman, and is both
educational and entertaining:

http://www.wcsscience.com/deck/ofcards.html

If this meets your needs, please let me know. I'll be glad to gather a
bit more info and post your answer.

And there is the ever popular

Pick a number and keep it to yourself...

OK now double that number

OK now add ummm say 7

Now take the number you have now and divide it by 2

Last but not least take the number that you started with and subtract
it from the number that you have now.

Now your number is 3

Ok we could round to 4 but your number is really 3.5

Thanks Steve

Here's how I would explain this enormous number:

Shuffle a different pack for each different way it can be shuffled. 
We're going to try laying them out on the ground to start counting
them.  Bridge cards are about 5.72cm wide and about 8.89cm high
(http://www.djmcadam.com/poker-bridge-cards.html), this gives an area
of around 50cm^2, which means we can fit 200 packs per square meter
(100cm*100cm=10000cm^2).

So let's start laying them out.

As you say the number of packs is 52*51*50*...

This number is around 8*10^67.  Since we can fit 200 per square meter,
we only need 4*10^65 square meters to lay out our cards.

Unfortunately the surface area of the entire earth is only 5*10^14 m^2
(http://www.vendian.org/envelope/dir1/earth_jupiter_sun.html), so
we're going to need to stack them on top of one another.  In fact we
will have to stack 8*10^50 packs on each point of the surface of the
entire earth.

A pack of cards is about 2cm high.  This means the piles will be
1.6*10^45 km tall.  Unfortunately the distance to the moon is only
384,403 km.  In fact the distance to the sun is only about 150,000,000
km (http://solarsystem.nasa.gov/planets/solarsys101.cfm)... 7 light
minutes.

How about the distance to the edge of the universe?  Well that's
around 15 billion light years... about 1.4*10^23 km.  So alas, we will
not be able to stack our cards in the entire universe. [in fact the
card pile would collapse into a black hole under its own gravity long
before then]

Just say we could buy extra universes as warehouses, for a penny per
universe.  We need about 10^22 warehouses, so it will cost us about
$100,000,000,000,000,000,000.  That's 100,000,000,000 billion dollars.
 The entire world GDP is about 40 000 billion dollars
(http://www.j-bradford-delong.net/TCEH/1998_Draft/World_GDP/Estimating_World_GDP.html
or http://216.239.59.104/search?q=cache:ms9Z6taeRcMJ:www.worldbank.org/data/databytopic/GDP.pdf+US+total+GDP&hl=en&ie=UTF-8).

So the entire world is going to have to work for about 2,500,000 years
in order to afford these universe warehouses to store our cards (and
remember they were cheap universes).

How long is 2,500,000 years?  Well, homo erectus probably came into
existence about 1,500,000 years ago
(http://www.wsu.edu:8001/vwsu/gened/learn-modules/top_longfor/timeline/timeline.html)...
so about a million years longer than that :-).