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

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) 6

(b) 18

(c) 12

(d) 9

Solution:

Since parallelogram needs two set of parallel lines

i.e selecting two parallel lines from a set of four can be done is ${ }^{4} C_{2}=\frac{4 \times 3 \times 2 !}{2 ! \times 2 !}=6$

and selecting two parallel lines from set of three parallel lines can be done in ${ }^{3} C_{2}=\frac{3 !}{2 !}=3$

∴ Number of parallelogram that can be formed is 6 × 3 = 18.