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Four married couples attend a wedding dinner. One of the couples brought along two children. Find the number of ways in which these ten people can be seated round a table if each couple must sit together.

I need to know the logic and thinking process behind how the answer is derived.

What I tried is:

First person has 10 seats to choose, second person 8 seats to choose and so on. Each couple can then seat on different sides.

10(8)(6)(4)(2^5)=61440

Correct answer is 1920

Another way of thinking I have is this: Consider each couple and the 2 children as each individual groups.

Total number of ways of arranging the 5 groups in a round table is (5-1)!=24

Then permutate each couple and children=2^5

so total number of ways = (2^5)24=768

I need to know the logic and thinking process behind how the answer is derived.

What I tried is:

First person has 10 seats to choose, second person 8 seats to choose and so on. Each couple can then seat on different sides.

10(8)(6)(4)(2^5)=61440

Correct answer is 1920

Another way of thinking I have is this: Consider each couple and the 2 children as each individual groups.

Total number of ways of arranging the 5 groups in a round table is (5-1)!=24

Then permutate each couple and children=2^5

so total number of ways = (2^5)24=768

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