Four Boxes, Min Three

Subtract the minimum 3 balls from each box first.

Use stars and bars on the remaining balls.

1. 1. Reduce

   Give each of 4 boxes 3 balls (12 total), leaving 8 balls to distribute freely.

2. 2. Stars and bars

   Number of ways is $\left(\genfrac{}{}{0ex}{}{8+4-1}{4-1}\right)=\left(\genfrac{}{}{0ex}{}{11}{3}\right)$.

   $$\left(\genfrac{}{}{0ex}{}{11}{3}\right)=165$$

Answer: 165