Permutations & Combinations
Grade None
Question:
<p>The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is</p>
<p style="display:inline">9</p>
<p style="display:inline">6</p>
<p style="display:inline">12</p>
<p style="display:inline">18</p>
Step-by-Step Solution
Key Concept: To form a parallelogram, you must select two lines from the first set of parallel lines and two lines from the second set using the multiplication principle of combinations.
<p>A parallelogram is formed by the intersection of a set of two parallel straight lines with another set of two parallel lines.<br />
<span class="math-tex">$\Rightarrow$</span> Total number of parallelograms formed<br />
= <sup>4</sup>C<sub>2</sub> <span class="math-tex">$\times$</span> <sup>3</sup>C<sub>2</sub> = 6 <span class="math-tex">$\times$</span> 3 = 18</p>
Correct Answer: D