Problem: In a shooting match, eight clay targets are arranged in two hanging columns of three targets each and one column of two targets. A marksman is to break all the targets according to the following rules: 1) The marksman first chooses a column from which a target is to be broken. 2) The marksman must then break the lowest remaining target in the chosen column. If the rules are followed, in how many different orders can the eight targets be broken? Solution: Not quite sure why this was a P8, but oh well. Simply consider the arrangements of the string $11122233$ where, each time a $k \in \{ 1,2,3 \}$ is red from left to right, the marksman shoots the bottom target on that column. It is clear that each string represents a valid ordering, and any ordering can be modeled with a string. The total arrangements of this string is given by the multinomial coefficient $\frac{8!}{3!3!2!} = 560$.