# Permutations/Combinations

#### oryxncrake

##### New member
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?

#### galactus

##### Super Moderator
Staff member
By the multiplication principle. 5*7*3=105

#### soroban

##### Elite Member

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

#### mmm4444bot

##### Super Moderator
Staff member
soroban said:

… Miss Scarlet did it in the ballroom with a candlestick.

Soroban, pleeeeze. This is a family-friendly web site.

#### chrisr

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

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

$$\displaystyle With\ 7\ choices\ of\ location,\ that's\ 60(7)=420.$$
[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.

$$\displaystyle Should\ we\ include\ self-termination?$$

#### soroban

##### Elite Member
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.