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Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations

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

$\begin{array}{1 1}(A)\;15\\(B)\;18\\(C)\;20\\(D)\;22\end{array} $

1 Answer

Toolbox:
  • $c(n,r)=\large\frac{n!}{r!(n-r)!}$
Let number of teams =n
No of matches =$nC_2$
$nC_2=153$
$\large\frac{n(n-1)}{2}$$=153$
$n^2-n=306$
$n^2-n-306=0$
$n^2-18n+17n-306=0$
$n=-17,18$
Hence $n=18$
Hence (B) is the correct answer.
answered May 16, 2014 by sreemathi.v
 

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