There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is :

Option 1) 9

Option 2) 11

Option 3) 12

Option 4) 7

Answers (1)

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

^{n}c_{r}=\frac{(n)!}{r!(n-r)!}

- wherein

Where 1\leq r\leq n

 

^{m}\textrm{C}_{2}\times 2-^{m}\textrm{C}_{1}\times ^{2}\textrm{C}_{1}\times 2=8y\\\\m(m-1)-4m=84\\\\\Rightarrow (m-12)(m+7)=0\\\\\Rightarrow m=12

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