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

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Solution

18.
If n is the number of teams, then
$^{n} C_{2} = 153$ to $n^{2}$ - n - 306 = 0
or (n - 18) (n + 17) = 0
$∴$ n = 18 $[∴ n \neq - 17] .$

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

18.If n is the number of teams, thennC2=153 to n2 - n - 306 = 0or (n - 18) (n + 17) = 0∴ n = 18 [∴n≠−17].

18.
If n is the number of teams, then
$^{n} C_{2} = 153$ to $n^{2}$ - n - 306 = 0
or (n - 18) (n + 17) = 0
$∴$ n = 18 $[∴ n \neq - 17] .$