Permutations (2 Viewers)

[Just.Snaz]

12.9 Maths in Focus
15. a) Nine beads are arranged randomly in a line. How many arrangements are possible?
b) If the beads are placed in a circle, how many ways can this be done?
c) The beads are arranged on a bracelet. How many different ways are possible?

answers: a) 362 880 b) 40 320 c) 20 160

I get the first two parts, but the last part.. well its 8!/2 but why? Isn't a bracelet the same as a circle?

Thanks guys

 

[AppleNader]

12.9 Maths in Focus
15. a) Nine beads are arranged randomly in a line. How many arrangements are possible?
b) If the beads are placed in a circle, how many ways can this be done?
c) The beads are arranged on a bracelet. How many different ways are possible?

answers: a) 362 880 b) 40 320 c) 20 160

I get the first two parts, but the last part.. well its 8!/2 but why? Isn't a bracelet the same as a circle?

Thanks guys

I think this might help


How many different color patterns are possible for the bracelet, where patterns are considered the same if turning one will produce the other, as shown here?

That's probably why you have to divide by 2!, to avoid double counting the same pattern.

 

[3unitz]

I get the first two parts, but the last part.. well its 8!/2 but why? Isn't a bracelet the same as a circle?

Thanks guys

because you can flip it round, and its still the same bracelet

 

[AppleNader]

Just.Snaz, don't thank us or anything.

 

[Just.Snaz]

Just.Snaz, don't thank us or anything.

lol I did. I thanked you in advance, but I'm actually still tryna figure it out..


so what you guys are saying is, without dividing by two, I've got all the arrangments repeated twice? Why?


THANKYOU SO MUCH I LOVE YOU ALL

 

[AppleNader]

lol I did. I thanked you in advance, but I'm actually still tryna figure it out..


so what you guys are saying is, without dividing by two, I've got all the arrangments repeated twice? Why?


THANKYOU SO MUCH I LOVE YOU ALL

Well like 3unitz said, you can flip a bracelet around but with the circle you're arranging it on a flat surface where you can't flip it over.

So you to avoid counting the same pattern when the braclet is flipped over you have to divide by two. Have a look at my diagram.

 

[lyounamu]

lol I did. I thanked you in advance, but I'm actually still tryna figure it out..


so what you guys are saying is, without dividing by two, I've got all the arrangments repeated twice? Why?


THANKYOU SO MUCH I LOVE YOU ALL

Circle is a permutation where you have a different combination. If you have a necklace where you have same colours, you will repeat the combination over again. That's why we divide it by two.

EDIT: Think of flipping as the above said.

 

[Just.Snaz]

ohhhhhhhhhhhh..... I get it

cause like if you have 4 beads for eg, you can have Blue, Green, Red, Yellow.. and Yellow, Red, Green, Blue.. and when you flip em around, they're both the same

Thank you

Edit: had colours wrong way round