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.

Step 1: 2 ways (corresponding to each color)

Step 2: As color of other sides got fixed

Step 3: Not possible => 0 ways as color of other sides got fixed and there will be one triangle which will have all sides

Step 4: rud on block

Step 5: => not possible => 0 ways (same reason as above)

Step 6: Only one way of colouring as color of other sides got fixed

Step 7: => 2 ways (corresponding to each color for shown figure)

Step 8: => total number of ways

Step 9: = 2 + 5c1 × 2 = 12 ways

Step 10: 1 ways of choosing 2 will active rides