Answer: P(none of them Europeans play against each other)=[tex]\frac{5}{14}[/tex]
Explanation:
Since there are 8 teams in which 3 are Europeans.
So, remaining 5 teams are not Europeans
We have to take 2 teams to pair up.
And we have a condition that neither of team is European.
So the favourable outcome =[tex]\binom{5}{2}[/tex]
and the total outcomes=[tex]\binom{8}{2}[/tex]
So, by using theprobability formula i.e.
P(E)=[tex]\frac{\text{No. of favourable outcome}}{\text{Total no. of outcomes}}[/tex]
P(getting none of European team play against each other)=[tex]\frac{\binom{5}{2}}{\binom{8}{3}}[/tex]
=[tex]\frac{5\times4}{8\times7}[/tex]
=[tex]\frac{5}{14}[/tex]
