Circular arrangements q (2 Viewers)

[=)(=]

 

[5uckerberg]

View attachment 34772

First question put the first child in and then how many spaces can he second child sit and then how many avaliable seats are avaliable for the third so that all three kids comply with social distancing.

 

[jimmysmith560]

Would this help?

Solution: Choose 3 out of the 6 possible slots for the children to be seated between 2 adults, then multiply by 3! for the children permutation, then multiply by (6-1)! for the 6 adults circular permutation.

Answer: 14400

 

[5uckerberg]

6 times 4 and then 6!

 

[=)(=]

For some reason i still cant get it, would it work if i tried fixing a child?

 

[Masaken]

For some reason i still cant get it, would it work if i tried fixing a child?

(someone please double check this im doubting myself)

In the circular arrangement, each child will be sitting in between two adults, so that no child with sit with another. We can pair a child with an adult so this means there will be three groups of adult+child, and three lone adults - 6 people in total since adult+child are regarded as one. To find the lone adults who will occupy the seat first, you will do 6 x 5 x 4. And then to find the children, 3 x 2 x 1. Multiply both together and you will get 6!

Then, since this is a circular arrangement, and to account for all the adults (lone adult, plus the adults in the adult+child group) remember that (6-1)! = 5!

So, the total would be 6!x 5! = 86400 - option D

 

[jimmysmith560]

Below is a different approach:



The answer is indeed (C).

 

[=)(=]

Below is a different approach:

View attachment 34785

The answer is indeed (C).

Not to sure about that diagram as it depicts 12 spots when there are just 9

 

[Masaken]

Not to sure about that diagram as it depicts 12 spots when there are just 9

It is the number of available spots a child can take, it doesn't mean there'll be a child in every space (once a child fills three of those circular spots there will be some adults in between two adults)

 

[=)(=]

Idk im just confused a

 

[yanujw]

@Masaken
Answer cannot be D because the way of arranging 9 people with no restriction is 8! < 86400

 

[Masaken]

@Masaken
Answer cannot be D because the way of arranging 9 people with no restriction is 8! < 86400

Ah, that makes sense. Been struggling with permutations and combinations as a topic currently, so I wasn't so sure. Thanks