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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Solution

The correct option is B 18
Let $n$ be the number of teams participated in the championship.
As every team played one match with each other then the total number of matches is 153.
So, $^{n} C_{2} = 153 \Rightarrow \frac{n (n - 1)}{2} = 153 \Rightarrow n (n - 1) = 306 \Rightarrow n (n - 1) = 18 \times (18 - 1) ∴ n = 18$

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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

The correct option is B 18Let n be the number of teams participated in the championship.As every team played one match with each other then the total number of matches is 153.So, nC2=153⇒n(n−1)2=153⇒n(n−1)=306⇒n(n−1)=18×(18−1)∴n=18