Question

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

• A. 18
• B. 12
• C. 9
• D. 6

Answer 1

Answer: (A)

Number of ways of choosing 2 parallel lines
from a set of four parallel lines $={}^4{C}_2$
Number of ways of choosing 2 parallel lines from a set of 3 parallel lines $={}^3{C}_2$
$\therefore$ Required number of ways $={}^4{C}_2\times {}^3{C}_2$
$=\frac{4\times 3}{2\times 1}\times 3$
$=6\times 3=18$