Question

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

• A. 17
• B. 18
• C. 9
• D. 13

Answer 1

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, ${}^n{C}_2=153\Rightarrow \frac{n(n-1)}{2}=153\Rightarrow n(n-1)=306\Rightarrow n(n-1)=18\times (18-1)\therefore n=18$