Expert: Paul Klarreich - 3/4/2009

Question
Can you tell me how many possible ticket combinations. Here's an example:
MTL   BUF                   
DET   COL  
CGY   PHI   
PHX   BOS   
NYR   NYI   
TOR   WAS   
EDM   OTT    
PIT   FLA   
CLB   NAS
MIN   SJ    
DAL   LA

Basically you have to pick one team from every match-up, i worked it out to 2,048 combinations but i also don't trust my math skills. Also, if you know a formula for calculating this in the future that would be great too.

Answer
Questioner:   kyle
Category:  Advanced Math
Private:  No
 
Subject:  Ticket Combination
Question:  Can you tell me how many possible ticket combinations. Here's an example:
MTL   BUF                   
DET   COL  
CGY   PHI   
PHX   BOS   
NYR   NYI   
TOR   WAS   
EDM   OTT    
PIT   FLA   
CLB   NAS
MIN   SJ    
DAL   LA

Basically you have to pick one team from every match-up, i worked it out to 2,048 combinations but i also don't trust my math skills. Also, if you know a formula for calculating this in the future that would be great too.
..........................................
This is an application of the Basic Counting Principle.  It says:

If you can do the first  thing   n1  ways.
If you can do the second thing   n2  ways.
If you can do the third thing    n3  ways.
If you can do the fourth thing   n4  ways.

etc.

Then the number of ways you do do them all (make all the choices) is the product of the numbers. [I.e. multiply all the numbers.]

So if each of those choices can be made 2 ways and there are 11 of them (by my count), then the number of possibilities is:


2^11 = 2048.

You got it.