Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a line. In how many ways can we color these lines by red or blue, so that no three of the points form a triangle with lines of

Question

Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a line. In how many ways can we color these lines by red or blue, so that no three of the points form a triangle with lines of the same color.

Quantrex Academy · Accepted Answer

Correct answer: 12

Case-I: 2 ways (corresponding to each color) As color of other sides got fixed Case-II: Not possible 0 ways as color of other sides got fixed and there will be one triangle which will have all sides rud on block Case-III: not possible 0 ways (same reason as above) Case-IV: Only one way of colouring as color of other sides got fixed 2 ways (corresponding to each color for shown figure) total number of ways =2+ ^5 C₁ 2=12 ways ^5 C₁ ways of choosing 2 will active rides

Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a line. In how many ways can we color these lines by red or blue, so that no three of the points form a triangle with lines of the same color.

Correct answer

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