$n$ number of balls are thrown randomly to $m$ number of bins, standing in a row. The balls are labeled as $1,2,3,....n$ and bins are also labeled as $1,2,3,...,m$. The probability of $i_{th}$ ball enters in the $j_{th}$ bin is $p_{ij}$. What is the expected number of balls per occupied bin when all $n$ balls are thrown simultaneously?

$n$ number of balls are thrown randomly to $m$ number of bins, standing in a row. The balls are labeled as $1,2,3,....n$ and bins are also labeled as $1,2,3,...,m$. The probability of $i_{th}$ ball enters in the $j_{th}$ bin is $p_{ij}$ where $\sum_{j=1}^{m}p_{ij}=1$ for all $i$. What is the expected number of balls per occupied bin when all $n$ balls are thrown simultaneously?