# 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:

$C_{{ 2}}(5)=\dbinom{ 5}{ 2}=\dfrac{ 5! }{ 2!(5-2)!}=\dfrac{ 5 \cdot 4 } { 2 \cdot 1 }=10 \ \\ \ \\ n_{1}={ { 5 } \choose 2 }=10 \ \\ \ \\ n=2 \cdot \ n_{1}+1=2 \cdot \ 10+1=21$

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