Permutations (1 Viewer)

[untouchablecuz]

Q1. Twelve differently coloured beads are arranged around a necklace. How many different arrangements are possible?

ALSO

Q2. Nine beads are arranged on a bracelet. How many different ways are possible?

1. Do I assume the necklace is circular? So the possible amount of arrangements would be 11! But the textbooks answer is completely different. Please help?

2. As above.

 

[independantz]

Q1. Twelve differently coloured beads are arranged around a necklace. How many different arrangements are possible?

ALSO

Q2. Nine beads are arranged on a bracelet. How many different ways are possible?

1. Do I assume the necklace is circular? So the possible amount of arrangements would be 11! But the textbooks answer is completely different. Please help?

2. As above.

You have to divide by 2 as the bracelet can be viewed from both sides, as a result you are over counting by a factor of 2

a) 11!/2
b 8!/2

 

[untouchablecuz]

What do you mean by, 'it can viewed from both sides'?

 

[undalay]

You can flip it around.

 

[independantz]

What do you mean by, 'it can viewed from both sides'?

For example if you have a bracelet with 4 different colored balls, if you view it from one way and then from the other, i.e turn it upside down they are essentially still int he same arrangement, however if you have people seated around a table well you can't really do that yeah? so you have to divide by 2 for circular arrangements that can be viewed from both sides.