Question

Answer the following:

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed

Answer 1

To form a parallelogram, we have to select any 2 of 4 parallel lines and any 2 of another 5 parallel lines for intersecting.

∴ the number of parallelograms which can be formed

= ⁴C₂ × ⁵C₂

= `(4!)/(2!2!) xx (5!)/(2!3!)`

= `(4 xx 3)/(2 xx 1) xx (5 xx 4)/(2 xx 1)`

= 6 × 10

= 60.