Permutations/Combinations

oryxncrake

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Joined
Oct 8, 2009
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7
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?
 

But I'm certain Miss Scarlet did it in the ballroom with a candlestick.

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

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

With 7 choices of location, thats 60(7)=420.\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.

Should we include selftermination?\displaystyle Should\ we\ include\ self-termination?
 
Hello, everyone!

If this is the game of CLUE, it already has a victim, Mr. Boddy.

The seven guests (Col. Mustard, Mrs. White, Professor Plum, etc.) are the suspects.

 
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