Solution

Given:

•There are two parallel lines in a plane.

• One line has 5 points.

•Another line has 4 points.

To find:

• The number of different triangles using the 9 points on two lines.

Approach and Working out:

A triangle is formed by 3 different points.

Hence, we need to select 3 different points from 9 different points.

But, there is a catch.

• Can you form a triangle if all the three points lie on one line??

Let us call the line having 5 points as L1 and line having 4 different points as L2.

Since three different points give only one triangle, this is a combination question.

Thus, the possible cases to form a triangle are:

• Select two points on L1 and one point on L2

• Select two points on L2 and one point on L1.

Total ways to form the triangle= \(^5C_2\)* \(^4C_1\) + \(^4C_2\)* \(^5C_1\)

Hence, option B is the correct answer.

Answer: B
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