Combination Symbol

 

 

The combination symbol is written as ⁿC_r,where

                                   

 

Here we introduce the combination symbol as it is an essential part of the binomial theorem. However, there are many other possible uses of the combination symbol, largely in permutations and combinations, which we do not cover in our site. Hence, we would like to state that the applications of the combination symbol is not limited to the binomial theorem.

 

Definition of the combination symbol:

                                                    

 

Using the idea of factorials, the combination symbol can be re-expressed as:

                                

 

  Proof:

                        

                  The properties of factorials is important in this algebraic proof.

 

 

Useful properties of the Combination Symbol

 

     

 

     Why? By definition,

       

 

         

 

       Proof:

                  

 

This proof involves techniques of algebraic manipulation as well as properties of factorials.