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**ANDS!** What you want is $\displaystyle n_1!*n_2!*n_3!$, where $\displaystyle n_1$ is the Character, $\displaystyle n_2$ is the room in the mansion, and $\displaystyle n_3$ is the weapon.

For example: Lets say Professor Plum we know is the murderer. He could have done it in any of the 7 rooms correct? So there are (at the moment) 7 possible scenarios for Plum to have committed the murder. But we also know he can use 3 weapons in each of the 7 scenarios: so thats three weapons in Room 1, three weapons in Room 2, three weapons in Room 3, etc. to three weapons in room 7 - for a total of 21 possible scenarios that Professor Plum (Character), could have gone somewhere (Room) and used a weapon (Weapon) to murder someone. But Plum isn't the only character. We have 5.

Thus you would use the basic methods of counting to find out the total possible scenarios that can play out here.

As an aside, remember what permutations and combinations are: Permutations are just an arrangement of $\displaystyle n$ objects, and combinations are the same arragement with uniqueness factored in.