A release-checked easy problem for training Multinomial Coefficient.
Question
A sniper is shooting at targets. There are $r$ columns of identical targets, with column $i$, $1 \leq i \leq n$, having $n_i$ targets in it stacked vertically. The sniper first selects a column and then shoots the lowest-hanging target in that column that is not broken. Once a column is out of targets, it is no longer able to be selected. In how many distinct orders can the sniper break all the targets? Solve this when $n = 5$ and $n_i = i$.
Practice focus
This Probability problem is tagged Multinomial Coefficient. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.