Question 607074
Larry, John, Peter, Brian, Trevor, Mike
<pre>
Pick one of the golfers, say Larry, as the chooser of 
his two team-mates. Any choice Larry makes for his two 
team-mates will determine both teams.  That's because
Larry will play with the two golfers he chose as 
team-mates, and the 3 that he didn't choose will make
up the other team.

The number of ways Larry can choose his 2 team-mates 
from the 5 is:

C(5,2), 5C2, {{{(matrix(2,1,5,2))}}}, i.e., the number of 
combinations of 5 things 2 at a time.

Different teachers and different text-books use different 
notations for this. Some just say "5 Choose 2". 

On the TI-83 and 84 calculators you type

5 nCr 2  then press ENTER.  (You get the nCr by pressing 
MATH, left arrow, 3).  

But regardless of what notation you use, or whether you use
the calculator, the formula {{{5!/(3!(5-3)!)}}} or  {{{(5*4)/(2*1)}}} you will get
10 ways.  Here they are, using only the golfers' initials:

 1. Team {L,J,P} and {B,T,F} play.
 2. Team {L,J,B} and {P,T,F} play.
 3. Team {L,J,T} and {B,P,F} play.
 4. Team {L,J,F} and {B,T,P} play.
 5. Team {L,P,B} and {J,T,F} play.
 6. Team {L,P,T} and {J,B,F} play.
 7. Team {L,P,F} and {J,B,T} play.
 8. Team {L,B,T} and {J,P,F} play.
 9. Team {L,B,F} and {J,P,T} play.
10. Team {L,T,F} and {J,B,P} play.

Edwin</pre>