# Tournament

How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the overall winner of the tournament?

Correct result:

n =  21

#### Solution:

$C_{{ 2}}(5)=\dbinom{ 5}{ 2}=\dfrac{ 5! }{ 2!(5-2)!}=\dfrac{ 5 \cdot 4 } { 2 \cdot 1 }=10 \ \\ \ \\ n_{1}={ { 5 } \choose 2 }=10 \ \\ \ \\ n=2 \cdot \ n_{1}+1=2 \cdot \ 10+1=21$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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