# Tournament

Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with each other?

Correct result:

n =  15

#### Solution:

$n_{1}=6 \cdot \ (6-1)/2=15 \ \\ C_{{ 2}}(6)=\dbinom{ 6}{ 2}=\dfrac{ 6! }{ 2!(6-2)!}=\dfrac{ 6 \cdot 5 } { 2 \cdot 1 }=15 \ \\ \ \\ n={ { 6 } \choose 2 }=15$

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