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

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

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

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.

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}$}}$$