Q. 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
Explanation
(b)
Let there are $n$ teams.
Each team play to every other team in $\ ^{n}C_{23}$ ways
$\therefore\ ^{n}C_{2} = 153$ (given)
$\Rightarrow \ \frac{n!}{(n - 2)!2!} = 153$
$\Rightarrow \ n(n - 1) = 306$
$\Rightarrow \ n^{2} - n - 306 = 0$
$\Rightarrow \ (n - 18)(n + 17) = 0$
$\Rightarrow \ n = 18\ \ \ \$($\because n$ is never negative)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.