There are two women participating with some m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the number of men be $n$. Each participant plays $2$ games with every other participant. The number of games played between men is $2 	imes \

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(B) Let the number of men be $n$. Each participant plays $2$ games with every other participant. The number of games played between men is $2 	imes \binom{n}{2} = 2 	imes \frac{n(n-1)}{2} = n(n-1)$. The number of games played between men and women is $2 	imes (n 	imes 2) = 4n$. According to the problem,$n(n-1) - 4n = 66$. $n^2 - n - 4n = 66 \Rightarrow n^2 - 5n - 66 = 0$. $(n-11)(n+6) = 0$. Since $n$ must be positive,$n = 11$. Total participants = $n + 2 = 11 + 2 = 13$.

Similar Questions

If the number of diagonals of a regular polygon of $n$ sides is $104$,then $n=$

If a polygon of $n$ sides has $275$ diagonals,then $n$ is

$A$ polygon has $35$ diagonals,then the number of its sides is

The number of shortest paths from point $A$ to $D$ (as shown in the figure) is:

There were two women participating in a chess tournament. Every participant played two games with every other participant. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is

Vedclass Test Series

Exam Paper Generator

Online Exam Module