Question:

<p><strong>Step 1:</strong> A parallelogram is formed by choosing 2 lines from the first family of <i>m</i> parallel lines and 2 lines from the second family of <i>n</i> parallel lines.</p><p><strong>Step 2:</strong> The number of ways to choose 2 lines from <i>m</i> lines is:</p><p>$$\binom{m}{2} = \frac{m(m-1)}{2}$$</p><p><strong>Step 3:</strong> The number of ways to choose 2 lines from <i>n</i> lines is:</p><p>$$\binom{n}{2} = \frac{n(n-1)}{2}$$</p><p><strong>Step 4:</strong> Each such pair of selections determines a unique parallelogram.</p><p><strong>Step 5:</strong> Therefore, the total number of parallelograms is:</p><p>$$\binom{m}{2} \times \binom{n}{2} = \frac{m(m-1)}{2} \times \frac{n(n-1)}{2} = \frac{mn(m-1)(n-1)}{4}$$</p>