Perms and combs (1 Viewer)

[eternallyboreduser]

For ring qs since you can "flip the ring around" why do u divide (n-1)! by 2! instead of multiplying it by 2! ? because wouldnt it double the number of ways if u can flip?

 

[SMARTYPANTS_SINGH]

I’m assuming you’re talking about the bracelet type questions. I think u divide by 2! Cause either way you flip it’s going to be the same pattern so that’s why you remove that repetition. It’s a similar concept to dividing by the number of repetitions in a word when you are finding the total arrangements.

 

[eternallyboreduser]

I’m assuming you’re talking about the necklace type questions. I think u divide by 2! Cause either way you flip it’s going to be the same pattern so that’s why you remove that repetition. It’s a similar concept to dividing by the number of repetitions in a word when you are finding the total arrangements.

But isnt (n-1)! the number of ways when u dont flip? Cos logically you wouldnt like flip a table and thats how u find the no. of ways for a table. So thags why im confused as to why youre dividing by 2!

 

[Hughmaster]

There are (n-1)! ways to arrange n objects on a circle. But arrangement on a ring corresponds to 2 arrangements on the circle (due to the flip). So there are less distinct arrangements on a ring.

 

[Average Boreduser]

For ring qs since you can "flip the ring around" why do u divide (n-1)! by 2! instead of multiplying it by 2! ? because wouldnt it double the number of ways if u can flip?

Consider, 3 people being arranged in a circle.
Note all cases. realise, that each of these cases revert back into 1 of 2 cases if you turn the table (using mulplication rule). Therefore, there is (n-1)! arrangements, i.e. (3-1)!=2!=2.

Now consider a bracelet and you try to arrange 3 beads. Notice that even though you get the same cases as when you arranged the people in a table. But... A bracelet can be flipped right? this would then make the arrangements to be just one case. Generically, this is represented as arrangements = (n-1)!/2 (divides by two to get rid of cases that repeat since you now have the ability to flip your 'bracelet', 'ring', wtv)