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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

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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?

AWESOMEEE  Jun 9, 2015

#4
+81090
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There are 5 girls......each plays five boys......5 x 5 = 25 games

CPhill  Jun 10, 2015
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#1
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i dont get the question. maybe a model (picture), or an explanation of the round-robin setup would do

TitaniumRome  Jun 9, 2015
#2
+17711
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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
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+18843
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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 ?

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

$$\small{\text{\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline & {Girl~1} & {Girl~2} & {Girl~3} & {Girl~4} & {Girl~5} & {Boy~1} & {Boy~2} & {Boy~3} & {Boy~4} & {Boy~5} \\ \hline {Girl~1}& - & {GG} & {GG} & {GG} & {GG} & {G}{B} & {G}{B} & {G}{B} & {G}{B} & {G}{B} \\ {Girl~2}& & - & {GG} & {GG} & {GG} & {G}{B} & {G}{B} & {G}{B} & {G}{B} & {G}{B} \\ {Girl~3}& & & - & {GG} & {GG} & {G}{B} & {G}{B} & {G}{B} & {G}{B} & {G}{B} \\ {Girl~4}& & & & - & {GG} & {G}{B} & {G}{B} & {G}{B} & {G}{B} & {G}{B} \\ {Girl~5}& & & & & - & {G}{B} & {G}{B} & {G}{B} & {G}{B} & {G}{B} \\ {Boy~1} & & & & & & - & {BB} & {BB} & {BB} & {BB} \\ {Boy~2} & & & & & & & - & {BB} & {BB} & {BB} \\ {Boy~3} & & & & & & & & - & {BB} & {BB} \\ {Boy~4} & & & & & & & & & - & {BB} \\ {Boy~5} & & & & & & & & & & - \\ \hline \end{array}}}$$

heureka  Jun 10, 2015
#4
+81090
+13