Two women and some men participated in a ches | vedclass

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

Question

(C) Let the number of men be $n$ and the number of women be $2$. The total number of participants is $n+2$.Each participant plays $2$ games with every

Vedclass · Accepted Answer

$(11, 13]$

Vedclass · Answer

(C) Let the number of men be $n$ and the number of women be $2$. The total number of participants is $n+2$.Each participant plays $2$ games with every other participant.The number of games played between men themselves:Each man plays $2$ games with every other $(n-1)$ man. The total number of games played by $n$ men is $\frac{n 	imes 2(n-1)}{2} = n(n-1)$.The number of games played between men and women:Each man plays $2$ games with each of the $2$ women,which is $2 	imes 2 = 4$ games per man. For $n$ men,the total number of games played with women is $4n$.According to the problem,the difference between these two is $66$:$n(n-1) - 4n = 66$$n^2 - n - 4n = 66$$n^2 - 5n - 66 = 0$$(n - 11)(n + 6) = 0$Since the number of men cannot be negative,$n = 11$.The value $n = 11$ lies in the interval $(11, 13]$. Thus,the correct option is $C$.

Similar Questions

The number of groups that can be made from $5$ different green balls,$4$ different blue balls,and $3$ different red balls,if at least $1$ green and $1$ blue ball is to be included.

How many $3$-digit numbers are there,with distinct digits,where each digit is odd?

Each section in the first year of a plus $2$ course has exactly $40$ students. If there are $5$ sections,in how many ways can a set of $4$ student representatives be selected,$1$ from each section?

$4$ alphabets $E, K, S$ and $V$,one in each,were purchased from a plastic warehouse. How many ordered pairs of alphabets,to be used as initials,can be formed from them?

How many numbers less than $1000$ can be made from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module