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.



Correct answer
12
Step-by-step solution
Case-I:

2 ways (corresponding to each color) As color of other sides got fixed Case-II:
Not possible 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 ways (same reason as above) Case-IV:
Only one way of colouring as color of other sides got fixed ways (corresponding to each color for shown figure) total number of ways ways ways of choosing 2 will active rides
2 ways (corresponding to each color) As color of other sides got fixed Case-II:
Not possible 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 ways (same reason as above) Case-IV:
Only one way of colouring as color of other sides got fixed ways (corresponding to each color for shown figure) total number of ways ways ways of choosing 2 will active rides