Question 122
There are 10 cards, each of which has two numbers, numbered $1$, $2$, $3$, $4$, $5$, written on it, and the numbers on any two cards are not exactly identical. The 10 cards are placed in five boxes labelled $1$, $2$, $3$, $4$, $5$, and a card with $i$ and $j$ written on it can only be placed in box $i$ or $j$. One placement is called “good” if there are more cards in box $1$ than in each of the other boxes. Then the total number of the “good” placements is ______.