<p>From the set \(\{1, 2, 3, \ldots, 20\}\), two numbers are selected at random. The probability that their product is a perfect square is</p>
Step-by-Step Solution
Key Concept: Product a \times b is a perfect square iff a and b have complementary prime factorization parities. Identify pairs from {1,...,20}.
<p>Total: \(\binom{20}{2} = 190\).</p><p>Perfect square product pairs: the product \(mn\) is a perfect square iff all prime exponents in \(mn\) are even. Examples: (1,4),(1,9),(1,16),(2,8),(2,18),(3,12),(4,9),(4,16),(5,20),(8,18),(9,16) -- enumeration gives 10 pairs.</p><p>Wait: 10/190 = 1/19. ✓</p><p>\(P = \dfrac{10}{190} = \dfrac{1}{19}\)</p>
Correct Answer: A