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There are 5 girls 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 a boy?

 Jun 9, 2015

Best Answer 

 #4
avatar+128079 
+13

There are 5 girls......each plays five boys......5 x 5 = 25 games

 

 

 Jun 10, 2015
 #1
avatar+2972 
0

i dont get the question. maybe a model (picture), or an explanation of the round-robin setup would do

 Jun 9, 2015
 #2
avatar+23245 
+3

Since each person plays every other person once, each girl will play four games against boys.

The total number of games that all girls play agains boys is 5 x 4 = 20 games.

 Jun 10, 2015
 #3
avatar+26364 
+13

There are 5 girls 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 a boy ?

 

$$\small{\text{$
\mathbf{ \rm{all ~games}=\binom{10}2 = 45 }
$}} \\
\small{\text{$
\mathbf{ \rm{only~ boys~games}=\binom52 = 10 }
$}} \\
\small{\text{$
\mathbf{ \rm{only~ girls~games}=\binom52 = 10 }
$}} \\
\small{\text{$
\mathbf{ \rm{one ~girl~one~boy~ games}=45-10-10 = 25 }
$}}$$

 

$$\small{\text{$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& \textcolor[rgb]{150,0,0}{Girl~1}
& \textcolor[rgb]{150,0,0}{Girl~2}
& \textcolor[rgb]{150,0,0}{Girl~3}
& \textcolor[rgb]{150,0,0}{Girl~4}
& \textcolor[rgb]{150,0,0}{Girl~5}
& \textcolor[rgb]{0,0,150}{Boy~1}
& \textcolor[rgb]{0,0,150}{Boy~2}
& \textcolor[rgb]{0,0,150}{Boy~3}
& \textcolor[rgb]{0,0,150}{Boy~4}
& \textcolor[rgb]{0,0,150}{Boy~5} \\
\hline
\textcolor[rgb]{150,0,0}{Girl~1}& - & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} \\
\textcolor[rgb]{150,0,0}{Girl~2}& & - & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} \\
\textcolor[rgb]{150,0,0}{Girl~3}& & & - & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} \\
\textcolor[rgb]{150,0,0}{Girl~4}& & & & - & \textcolor[rgb]{150,0,0}{GG} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} \\
\textcolor[rgb]{150,0,0}{Girl~5}& & & & & - & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} & \textcolor[rgb]{150,0,0}{G}\textcolor[rgb]{0,0,150}{B} \\
\textcolor[rgb]{0,0,150}{Boy~1} & & & & & & - & \textcolor[rgb]{0,0,150}{BB} & \textcolor[rgb]{0,0,150}{BB} & \textcolor[rgb]{0,0,150}{BB} & \textcolor[rgb]{0,0,150}{BB} \\
\textcolor[rgb]{0,0,150}{Boy~2} & & & & & & & - & \textcolor[rgb]{0,0,150}{BB} & \textcolor[rgb]{0,0,150}{BB} & \textcolor[rgb]{0,0,150}{BB} \\
\textcolor[rgb]{0,0,150}{Boy~3} & & & & & & & & - & \textcolor[rgb]{0,0,150}{BB} & \textcolor[rgb]{0,0,150}{BB} \\
\textcolor[rgb]{0,0,150}{Boy~4} & & & & & & & & & - & \textcolor[rgb]{0,0,150}{BB} \\
\textcolor[rgb]{0,0,150}{Boy~5} & & & & & & & & & & - \\
\hline
\end{array}$}}$$

 

 Jun 10, 2015
 #4
avatar+128079 
+13
Best Answer

There are 5 girls......each plays five boys......5 x 5 = 25 games

 

 

CPhill Jun 10, 2015

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