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There are  5vgirls and 5 boys in a chess club. The club holds a round-robin tournament in which every player plays against every other player exactly once.

In how many games does a girl play against another girl?

 Jan 13, 2019
 #1
avatar+101431 
+1

10 games.....

 

To see this, note that the 5th girl plays 4 other girls

The 4th girl plays 3 other girls

The 3rd girl plays 2 other girls

The second girl plays 1 other girl

 

So...4 + 3 + 2 + 1  =  10

 

Another way to see this is to count the number of sets formed by choosing any 2 girls from 5....this is

 

C(5, 2)  =  10   

 

cool cool cool

 Jan 13, 2019
edited by CPhill  Jan 13, 2019
 #2
avatar+533 
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thank you!!!

asdf335  Jan 13, 2019

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