Question

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines.
1. 18
2. 24
3. 32
4. 36

Answer 1

Correct Answer - Option 4 : 36

Concept used :

Number of parallelograms when n parallel lines intersect n parallel line = ⁿc₂ × nc₂

Calculations :

Here 4 parallel lines are intersecting 4 parallel lines so n will be 4 

Total number of parallelogram = ⁴c₂ × ⁴c₂

⇒  (4!/(2! × (4 - 2)!) × (4!/(2! × (4 - 2)!)

⇒ (4!)/(2! × 2!) × (4!)/(2! × 2!)                      (n! = n.(n - 1).(n - 2)..........1) 

⇒ 36 

∴ Option 4 will be the correct choice.