Question 8
(SPA 2) 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,
$$|N_i(t)-N_j(t)|\lt 2,\qquad i\ne j,\qquad i,j=1,2,\ldots\ .$$
$$|N_i(t)-N_j(t)|\lt 2,\qquad i\ne j,\qquad i,j=1,2,\ldots\ .$$