New-York tribune., 1918-09-29
Cards
II T IS fact that the total possible mum.
Der Of combinations Of the ffty.tvo
l. playing cards is so vast that II be.

L Is fact rhRt tne total possible mum.
Der of combinations Of the ffty.two
IL playing cards is so vast that It be.
comes impossible to frame a theory
covering all cases, even when the attempt Is
aided by classifying the cases.
AS one instance Of this, the fairly well
known fact may be mentioned tnat in
game like whist or bridge, where each player
receives hand of thirteen cards, selected
from the ffty-two, the total possible num-
Der of different hands that may thus be
selected is greater than 100000, 100000. The
exact number is 635, ,013 ,559, 500.
This number, however, large though It
may appear, becomes not merely small but
absolutely insignificant when compared with
the total number of arrangements in which
the ffty-two cards rsay be placed after the
shuttle To quote the whole of this number
would take too great a space, but it may be
mentioned that it begins with eighty and
is followed by sixty-six other figures
Let US suppose that 2,OOO,OOO,OOO of hu.
man beings, each supplied with pack OF
cards, were to attempt actually to produce
every possible arrangement of the ffty-two
cards. 1t is further to be supposed that
they work ceaselessly, without rest day or
night, from years end to years end, at the
rate OF one new arrangement per second for
each person during period of 100000 years
It should be noted that the entire popu-
lation of thc earth to-day is estimated to be
in the neighborhood of 1,600000,O00. The
hypothesis from which we start Is, there.
fore, that a population onequarter mon
than that which now exists has spent is
whole time during an interval more thai
fifty times the duration of the Chrlstsl
era in shutting cards at the rate of one
shuttle per second, or more than Sl00OOW
shuf1es in each year per head. In view Of
such figures the reader may we'll ask hoF
many times the total number of arrange.
amount of sustained, though ili-directed
human effort The answer is, Not once.
Let it be assumed that the whole vas.
number of arrangements produced by the
human race as above is symbolized by one
drop of water. Then how much water would
be required to symbolic the total number
possible? If this question is put to one, he
might we'll say: "Surely a glass Of water
ought to be enough!" No. "a bathful Of
water, them" No. "a large reservoir"
No. You must enlarge your conceptions, or
you will never reach the truth "The At
lantic Ocean, then? The number Of drops
in that will surely be sufficient"
But the number of drops of water in the
Atlantic Ocean is not sufficient, nor Will "
become so even when we add to the Atlantic
the Pacific Ocean and all the other oceans
seas, lakes, and, in fact, all the rest OF the
water on our globe. Nor would the Whole
earth, made from centre TO surface OF water
be sufficient. Nor would the whole SUI
similarly constituted suffice. Incredible s'
it may seem, to obtain a volume Of wa's'
containing a sufficient number of drops "
IS necessary to imagine a globe OF wa's'
with q diameter equal to 7,02500OOO miles
After the evidence comes the SUMMING
up. Thus, firstly, we take one drop o. water
to represent the whole result of sustaihsu
energy of the human race or, lndeea' ni0''
than the present number thereof), direc'eu
at breakneck speed to only one ools''
throughout an interval of time extehuIDs
not into the dawn of history, but beyond u
into period when man had probably Nv,
established his mastery over the snim''
creation.
And, secondly. we find that, though 'n''
one drop of water represents a result )"
enormous that it can hardly be graspeo's ~
the total result to be obtained is stu -
far off that to represent it on the same s'''
requires what is almost described IS
watery universe.
The result obtained is SO surprising 'A',
it will be useful to set out the calcula'V,.
by which it is reached, so as to show thss
is really correct. In the first place. ~
method by which the total number Of
rangements of the hfty-two cards is eS''
lated can be readily explained. For any Wv
of the fftytwo may be chosen as the w
card, and when some card has been ch'''-
then any one of the fifty-one remaH,4.
cards can be chosen as second card, 50 We
the two first cards may be chosen IN o'u''
in ffty-two times ffty-one, or 1852 wss'
There then remain fifty cards, any one.
which may be selected as third card i',
which it results that the three first cav, N.s
can be chosen in order in fifty times z''S.'
or 132,6o0 ways. Proceeding thus, 1t IL ".
dent that the total number of arrangeme,..
of the tifty-two cards can be calcula'eu :
multiplying together all the numbers p's
two, fifty-one, fifty, etc. down to one.