ILL 1983 Problem 58

In a test, $3n$ students participate, who are located in three rows of $n$ students in each. The students leave the test room one by one. If $N_1(t), N_2(t), N_3(t)$ denote the numbers of students in the first, second, and third row respectively at time $t$, find the probability that for each t during the test, $$|N_i(t) - N_j(t)| < 2, i \neq j, i, j = 1, 2, \dots .$$