<p>If <strong>x</strong> < 4 < <strong>y</strong> and <strong>x</strong>, <strong>y</strong> ∈ {1, 2, 3, ..., 10}, then find the number of ordered pairs (<strong>x</strong>, <strong>y</strong>).</p>
Step-by-Step Solution
Key Concept: Use the multiplication principle: count choices for x (all values less than 4) and y (all values greater than 4) separately, then multiply.
<p><strong>Solution:</strong> We have <strong>x</strong> < 4 < <strong>y</strong>, where <strong>x</strong>, <strong>y</strong> ∈ {1, 2, 3, ..., 10}</p><p>Therefore, <strong>x</strong> ∈ {1, 2, 3} and <strong>y</strong> ∈ {5, 6, 7, 8, 9, 10}</p><p>Here, <strong>x</strong> has 3 options and <strong>y</strong> has 6 options.</p><p>By the multiplication rule:</p><p>Number of ordered pairs = 3 × 6 = <strong>18</strong></p>
Correct Answer: b