Let n ≥ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line

Question

Let n &#8805; 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is ________

Quantrex Academy · Accepted Answer

Correct answer: 0

Number of red lines = n C 2 - n Number of blue lines = n Hence, n C 2 - n = n n C 2 = 2 n n n - 1 2 = 2 n n - 1 = 4 ⇒ n = 5 .

Let n ≥ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is ________

Correct answer

Step-by-step solution

More from Permutation and Combination

Let n &#8805; 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is ________

Correct answer

Step-by-step solution

More from Permutation and Combination

Let n ≥ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is ________