Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
Question:
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
Solution:
A parallelogram is formed by choosing two straight lines from a set of four parallel lines and two straight lines from a set of three parallel lines.
Two straight lines from the set of four parallel lines can be chosen in 4C2 ways and two straight lines from the set of three parallel lines can be chosen in 3C2 ways.
$\therefore$ Number of parallelograms that can be formed $={ }^{4} C_{2} \times{ }^{3} C_{2}=\frac{4 !}{2 ! 2 !} \times \frac{3 !}{2 ! 1 !}=6 \times 3=18$
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