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6.Permutation and Combination
medium
There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by $66$ the number of games that the men played with the women. The number of participants is
A
$6$
B
$11$
C
$13$
D
None of these
Solution
(c) Let there be $n$ men participants. Then the number of games that the men play between themselves is $2\;.{\;^n}{C_2}$ and the number of games that the men played with the women is $2.\;(2n)$.
$\therefore $$2.{\;^n}{C_2} – 2\;.\;2n = 66$ (By hypothesis)
$ \Rightarrow $${n^2} – 5n – 66 = 0 \Rightarrow n = 11$
$\therefore $ Number of participants $ = 11\;{\rm{men}} + 2\;{\rm{women}} = 13$.
Standard 11
Mathematics
