Let n 2 be an integer. Suppose that there a | vedclass

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(C) The total number of ways to connect $n$ stations in pairs is given by the combination formula ${}^{n}C_{2}$.The number of blue lines corresponds t

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$201$

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(C) The total number of ways to connect $n$ stations in pairs is given by the combination formula ${}^{n}C_{2}$.The number of blue lines corresponds to the number of sides of the polygon formed by the $n$ stations,which is $n$.The number of red lines corresponds to the number of diagonals of the polygon,which is given by ${}^{n}C_{2} - n$.According to the problem,the number of red lines is $99$ times the number of blue lines:${}^{n}C_{2} - n = 99n$Substituting the formula for ${}^{n}C_{2}$:$\frac{n(n-1)}{2} - n = 99n$Dividing both sides by $n$ (since $n > 2$):$\frac{n-1}{2} - 1 = 99$$\frac{n-1}{2} = 100$$n - 1 = 200$$n = 201$

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