You're playing a fantasy game that allows you to create your own character. There are 5 options for the race of
the character, and there are 3 options for the character's main tool
If you randomly choose the race and the tool, which of these diagrams can be used to find all of the possible
outcomes?

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."