Permutations/Combinations

hi

i don't know where else to post this but i need some help on a textbook question i was given about combinatorics.

there is a game that involves a murderer, a mansion, and the weapon used to commit the murder. there are 5 characters in all, 7 rooms in the mansion, and 3 weapons.

the question is.. how many kinds of guesses can i make from choosing one character, one mansion room, and one weapon?

also, is this question a permutation or combination?

By the multiplication principle. 5*7*3=105

\(\displaystyle Any\ character\ can\ kill\ any\ of\ the\ 4\ other\ characters,\)
\(\displaystyle that's\ 20\ possible\ murders\ if\ they\ are\ all\ potential\ murderers\ and\ victims.\)

\(\displaystyle Using\ any\ of\ the\ 3\ weapons,\ all\ deadly\ in\ some\ way,\)
\(\displaystyle that's\ 20(3)=60\ possible\ ways\ to\ commit\ 20\ killings,\)

\(\displaystyle With\ 7\ choices\ of\ location,\ that's\ 60(7)=420.\)
[sup:3kum0bnp]5[/sup:3kum0bnp]P[sub:3kum0bnp]2[/sub:3kum0bnp][sup:3kum0bnp]3[/sup:3kum0bnp]C[sub:3kum0bnp]1[/sub:3kum0bnp][sup:3kum0bnp]7[/sup:3kum0bnp]C[sub:3kum0bnp]1[/sub:3kum0bnp]=20(3)(7)=420.

\(\displaystyle Should\ we\ include\ self-termination?\)