in a football championship 153 matches were played. every team played one match with each other. the number of team participating in the championship

CBSE Class 11-science Answered

in a football championship 153 matches were played. every team played one match with each other. the number of team participating in the championship

Asked by Piyush Gupta | 09 Aug, 2010, 12:00: AM

Expert Answer

Dear Student.

Let the number of teams be N namely T₁, T₂ , . . . T_N.

Since, each team played one game with the other game, so T₁ played (N-1) games, T₂ played (N-2) games and so on.

Hence, total number of games being played is (N-1) + (N-2) + . . . + 1 + 0 = N(N-1)/2

The total number of games being played is given as 153.

=> 153 = N(N-1)/2

=> 306 = N² - N

=> N² - N - 306 = 0

Solving this quadratic equation, we get N = 18 or N = -17

But as number of teams can not be negative, therefore total number of teams in the tournament is 18.

Regards Topperlearning.

Answered by | 30 Nov, 2017, 11:35: AM

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