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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

Consider five points in the plane, with no three of them collinear....

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.Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by aConsider five points in the plane, with no three of them collinear. Every pair of points among them is joined by aConsider five points in the plane, with no three of them collinear. Every pair of points among them is joined by aConsider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a

Correct answer

12

Step-by-step solution

Case-I: Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a
2 ways (corresponding to each color) As color of other sides got fixed Case-II:Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a
Not possible ∴0\therefore 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:Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a
∴\therefore \quad not possible ∴0\therefore 0 ways (same reason as above) Case-IV:Consider five points in the plane, with no three of them collinear. Every pair of points among them is joined by a
Only one way of colouring as color of other sides got fixed ∴2\therefore \quad 2 ways (corresponding to each color for shown figure) ∴\therefore \quad total number of ways =2+5C1×2=12=2+{ }^5 C_1 \times 2=12 ways 5C1{ }^5 C_1 ways of choosing 2 will active rides
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