What an "Exam"

$N$ students filled their forms for a competitive exam. The Probability that exactly $r$ students will not appear in the exam is proportional to $r$ . If the probability that out of remaining $n-r$ students, exactly $i$ students are selected is proportional to $i$ . If the probability of 2 students finally selected can be represented as:

$\dfrac 8{n(n+1)} \left [ n\left (\dfrac1t - \dfrac1n \right) - \left ( \dfrac13 + \dfrac14 + \cdots + \dfrac1n \right) \right] ,$

for some constant $t$ , find $t$ .