+0  
 
0
644
4
avatar+1278 

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?

AWESOMEEE  Jun 9, 2015

Best Answer 

 #4
avatar+78577 
+13

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

 

 

CPhill  Jun 10, 2015
Sort: 

4+0 Answers

 #1
avatar+3088 
0

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

TitaniumRome  Jun 9, 2015
 #2
avatar+17653 
+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.

geno3141  Jun 10, 2015
 #3
avatar+18712 
+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}$}}$$

 

heureka  Jun 10, 2015
 #4
avatar+78577 
+13
Best Answer

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

 

 

CPhill  Jun 10, 2015

7 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details