# Math Permutations and Combinations

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#1
Hi all, I've been having some difficulty with understanding the solution to this maths question. I would really appreciate if someone could help me with it!

Three couples who each have a child are to be seated at a round table with ten secured seats. Mr Bean, who knows the three families well, is invited to take a seat at the table. Find the number of ways to seat the ten people if each child is to be seated adjacent to both his or her parents.

Solution:
Consider each couple and their child as a unit.
Number of ways of arranging 4 distinct units in a circle = 3!
Each couple can arrange amongst themselves in 2! ways.
Number of ways in which each child is seated between their parents = 3! x 2^3 = 48

Why isn't there a need to multiply the 48 by an additional 2? doesn't the position of the child need to be taken into account e.g. child parent parent and parent parent child?

0
6 months ago
#2
Hey there,

if you are facing any difficulties with anything please feel free to come over at Tripleconnect.co . At triple connect we connect students together so they can teach others and understand concepts. It is a free service to use, I am sure that we can definitely match you with someone to help you with your situation.
0
6 months ago
#3
(Original post by thebluhood)
Hi all, I've been having some difficulty with understanding the solution to this maths question. I would really appreciate if someone could help me with it!

Three couples who each have a child are to be seated at a round table with ten secured seats. Mr Bean, who knows the three families well, is invited to take a seat at the table. Find the number of ways to seat the ten people if each child is to be seated adjacent to both his or her parents.

Solution:
Consider each couple and their child as a unit.
Number of ways of arranging 4 distinct units in a circle = 3!
Each couple can arrange amongst themselves in 2! ways.
Number of ways in which each child is seated between their parents = 3! x 2^3 = 48

Why isn't there a need to multiply the 48 by an additional 2? doesn't the position of the child need to be taken into account e.g. child parent parent and parent parent child?

The child must be between its parents, so parent-child-parent.
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