Question

The maximum number of rectangles that can be formed from a set of 5 parallel lines intersecting another set of 6 parallel lines is __.

Answer 1

To form a rectangle we need four intersecting lines.

The first two parallel lines can be selected ${}^5{C}_2$ ways and other two parallel lines can be selected in ${}^6{C}_2$ ways.

Total number of parallelogram which can be formed = ${}^5{C}_2$ $\times$ ${}^6{C}_2$ ₌ 10 $\times 15=150$