Scheduling five students into fifteen slots

Over the coming month there are $15$ meeting slots, and you need to meet each of $5$ students exactly $3$ times, one student per slot, so every slot gets used. One particular student cannot make the first slot. How many valid schedules are there?

$134{,}534{,}400$. A schedule is a word using each of the five student labels three times, so there are $\tfrac{15!}{(3!)^5}$ in total. By symmetry each student is equally likely to occupy slot one, so $\tfrac45$ of these avoid the restricted student there: $\tfrac45\cdot168{,}168{,}000$.