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At a circular table for eight will sit two children

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by M7MBA » Mon Feb 26, 2018 1:43 am
At a circular table for eight will sit two children, their two parents, and the two parents of each of the children's parents, eight people in total. The children will sit together, the children's two parents will sit next to the children, one on either side of the two children, and the parents of each of the children's parents will sit next to each other beside the person who is their child. Given the restrictions, in how many ways can the people be arranged around the table.

(A) 8
(B) 16
(C) 64
(D) 96
(E) 1440

The OA is the option B.

Experts, how can I solve this question? Is there an easy way? Can you help me? Thanks in advanced.
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by regor60 » Tue Feb 27, 2018 10:07 am
M7MBA wrote:At a circular table for eight will sit two children, their two parents, and the two parents of each of the children's parents, eight people in total. The children will sit together, the children's two parents will sit next to the children, one on either side of the two children, and the parents of each of the children's parents will sit next to each other beside the person who is their child. Given the restrictions, in how many ways can the people be arranged around the table.

(A) 8
(B) 16
(C) 64
(D) 96
(E) 1440

The OA is the option B.

Experts, how can I solve this question? Is there an easy way? Can you help me? Thanks in advanced.
Pick the abbreviations of your choice to represent each person and write down according to question, so:

C1 and C2 children
P1 and P2 parents
G11, G12 parents of P1
G21 and G22 parents of P2

So, one ordering is as follows: G11 G12 P1 C1 C2 P2 G21 G22

Now, from the wording the GGPs are a package deal, wherever P moves to so do the G's.

Start with the two children, they can be arranged two ways: C1 C2 or C2 C1 so 2 ways

Within each GGP package the grandparents can be arranged two ways so 2 ways for each package means 2 x 2 = 4 ways

Finally the GGP packages can be swapped to either side, so 2 ways

Totalling: 2x4x2 = 16, B
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