Math Symbol for C

Date: 12/15/97 at 22:50:24
From: Andrew Valovcin
Subject: Re: Math symbol for C

This is my first time to your site and I find it very interesting and
enjoyable. I am puzzled by one symbol of typing math. What does the 
upper case letter C mean? Like in (2 C 1) (3 C 1) / (47 C 2) = 6/1081. 
I can't figure it out and before I get any more frustrated I thought 
I'd better write to you.

Thanks for your help.

Date: 12/17/97 at 08:12:11
From: Doctor Anthony
Subject: Re: Math symbol for C


The symbol nCr stands for the number of combinations of r things that 
can be formed from n different things. 

If you look in any textbook on probability and statistics you will 
find that permutations and combinations will feature a good deal in 
the early chapters. Modern text books now use a different notation for 
nCr, but it is written on two lines, the n above the r and with 
brackets around them but no line between.  This notation is not 
suitable for ascii presentation, so we have to revert to the older nCr 
notation.  In ascii we also use C(n,r) to mean the same thing, and 
this has advantages if we are working with numbers as the numbers 
themselves stand out more clearly.

                          10!
  10 C 4  =  C(10,4)  = ------   =  210
                         4! 6!

and if we are dealing with permutations, or arrangements, of 4 things 
that could be formed from 10 different things, then we write:

                        10!
  10 P 4 =  P(10,4) =  -----   =  5040
                         6!

The derivation of these expressions is straightforward and you will 
find them explained in almost any textbook on probability.  If you 
still have difficulty understanding them, write back.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/