In a football championship,there were played | vedclass

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(B) Let the number of teams be $n$.Since every team plays one match with every other team,the total number of matches is given by the combination form

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(B) Let the number of teams be $n$.Since every team plays one match with every other team,the total number of matches is given by the combination formula $^nC_2$,which represents choosing $2$ teams out of $n$ to play a match.Given that the total number of matches is $153$,we have:$^nC_2 = 153$$\frac{n(n - 1)}{2} = 153$$n(n - 1) = 306$$n^2 - n - 306 = 0$Solving the quadratic equation using the quadratic formula or factorization:$(n - 18)(n + 17) = 0$Since the number of teams cannot be negative,we have $n = 18$.Therefore,the number of teams participating is $18$.

In a football championship,there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is

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