From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: Probability question
Date: 21 Jul 1998 05:51:18 GMT

In article <6ojll2$ol6$1@nnrp1.dejanews.com>,  <skataba@my-dejanews.com> wrote:
>Here is a probability question. If you randomly draw 15 cards from a deck of
>the card game called "Set", what is the probability of having three 5-card
>"sets"? 

I don't know what a "5-card set" is; the game is usually played with rules
which define a "set" to have cardinality 3.

The makers of the Set game have a website which addresses a few of the 
points of interest; it's
	http://www.setgame.com
I have a few saved newsgroup posts at
	http://www.math.niu.edu/~rusin/uses-math/games/other

The game may be described to a mathematician as the search for lines
among randomly-selected sets of points in the affine space  A  of
dimension 4 over GF(3). The question you meant to ask was perhaps
something equivalent to, "Given 15 randomly selected points in  A, 
what is the probability that they form five lines?"

I don't know the answer to that question. There are (81 choose 15)
such sets of points; there are 1080 lines in A, and so roughly (1080
choose 5) sets of 15 points which form 5 lines. The ratio of these
binomial coefficients is about 1/671. But this is actually an
overcount, since there are some sets of 15 points which may be
partitioned into 5 lines in more than one way, and some sets of 5
lines which are not disjoint (and thus don't encompass 15 cards). 

You might get a better response on rec.games.abstract.

dave