Total cases = $^nC_2$. For favorable cases, let $a = 9$, $b = 9$. Find $i$ such that $|i - j| ≤ 3$ (must be an integer).
Step-by-Step Solution
Key Concept: Enumerate all pairs satisfying the distance constraint and divide by total pairs
With $a = 9$ and $b = 9$, the favorable cases where $|i - j| ≤ 3$ are enumerated as: if $i = 1$ then $j ∈ \{2,3,4\}$; if $i = 2$ then $j ∈ \{1,4,5\}$; ... if $i = 6$ then $j ∈ \{5,7,9\}$ and no such value of $j$ is possible. Hence favorable cases = 28. Required probability = $\frac{28}{^9C_2} = \frac{28}{36} = \frac{14}{55}$.
Correct Answer: 1