SOLUTION: Eight people enter a racquetball tournament in which each person must play every other person exactly once. Determine the total number of games that will be played?

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Question 885130: Eight people enter a racquetball tournament in which each person must play every other person exactly once.
Determine the total number of games that will be played?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It would be all possible pairings of the 8 players
this is the combination of 8 objects taken 2 at a time
+8%21+%2F+%28+2%21+%2A%28+8+-+2+%29%21+%29+
+8%21+%2F+%28+2%21+%2A+6%21+%29+
+%28+8%2A7%2A6%2A5%2A4%2A3%2A2%2A1+%29+%2F+%28+2%2A1%2A6%2A5%2A4%2A3%2A2%2A1+%29+
+%28+8%2A7+%29+%2F+%28+2%2A1+%29++=+28+
------------------------
check:
They are:
A B C D E F G H
-------------
A B
A C
A D
A E
A F
A G
A H
---------
B C
B D
B E
B F
B G
B H
--------
C D
C E
C F
C G
C H
--------
D E
D F
D G
D H
---------
E F
E G
E H
---------
F G
F H
----------
G H
----------
This is:
+7+%2B+6+%2B+5+%2B+4+%2B+3+%2B+2+%2B+1+=+28+
OK