Discrete Math Problem...am I correct?

[Xenon14]

It is Friday night and you are up watching late night television. An infomercial comes on the screen. "Don't be left out of this bracelet wearing craze. Our bracelets have 12 different color beads and sell for only $9.99. Each bracelet is unique. No two are alike. Buy yours today. Hurry, quantities are limited."
If the company has 12 different colors of beads and exactly one bead of each color must be used to make a bracelet, how many different bracelets can be made?

BONUS: If there are n different colors of beads and exactly one bead of each color must be used to make a bracelet, how many different bracelets can be made?

(okay...so i'm guessing since a bracelet is a circle, which means that 1 bead has to be moved around an extra time... to answer both the problem and the bonus... I'm thinking the equation is (n-1)! ) Am I correct?

 

[piku]

Get to bed slacker!

 

[marketsons1985]

Correct me if I'm wrong, but wouldn't it just be 12!

Because visualize the "X" as a bead

X X X X X X X X X X X X

Now, how many ways can the first be? 12
Second? 11,

etc. etc.

It wouldn't matter if the bead was moved around, that would just be another permutation of it

[Edit] What grade are you in?

 

[Mday]

how many beads are there?

 

[RichieZ]

HAHA! This is permutation junk, learned it for 5 mins for the SAT II Math IIc, and then i forgot it!

 

[marketsons1985]

Mday, I assumed that the statemen <<Our bracelets have 12 different color beads >>
meant there's 12 different colored beads on the bracelets....


of course, when you assume, you make an ass out of you and me......

 

[trmiv]

Wait, are these ankle bracelets or wrist bracelets?

 

[Capn]

You need to know the number of bead permutations. This is easy. I suggest you go to this site.

linky linky

 

[kwan]

you got it right 12!/12 12x11x10....x1/12

if you have 12 beads colors qwertasdfzx (each letter is a color)

chose one bead (we'll say w) that leaves 11 colors left.

then if you move the first bead to the end you have the same bracelet. you can move the bead to the end 12 times. so you divide by 12.

bonus: n!/n or (n-1)! same logic from above

-dan

&quot;DISCRETE SUX&quot; -Pascal

NOTE: for those of you who read this b/f the edit, i didn't read the whole problem. i'm stupid

 

[Xenon14]

Dude, but doesn't the fact that it's a circle limit the 12! combination... this is a bracelet, not a line up... so the 1st color and the 12th color are next to each other.... clearly it has to be (n-1)!; in this case 11!

 

[marketsons1985]

Ok, i got it now