Total cases = $^nC_2$. The number of favorable cases when $j$ is placed in pth of a is $^nC_1 × C_{j-1}^1$. Find required probability.
Step-by-Step Solution
Key Concept: Counting favorable arrangements using combination formulas and computing conditional probability
Total cases = $^{12}C_2 = 66$. For favorable cases when $j$ is placed in the $p$th position, we count $\sum C_{j-1}^1 = 71$. The required probability is $\frac{71}{11} = \frac{1}{100}$.
Correct Answer: 2