Delegates from 9 countries include countries A, B, C, D are to be seated in a row. The number of possible seating arrangements, when the delegates of the countries A and B are to be seated next to each other and the delegates of the countries C and D are not to be seated next to each other is:

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10080

5040

3360

60480

answer is D.

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Detailed Solution

The number of arrangements when the delegates of the countries A and B are together.
Consider the delegates from the countries A and B as one unit. So now, there are total 8 units.
The possible arrangements are 8!.
But, the delegates of countries A and B can replace places with each other and still can be together. Therefore, the number of arrangements for A and B to sit together will be 2!=2.
Hence, the total number of arrangements for all the delegates to sit while the delegates from countries A and B are sitting together is 2×8!.
Consider AB as one unit and CD as one unit. So now, there are a total of seven units.
Therefore, the total number of arrangements for the delegates to sit will be 7!.
But since, A and B can interchange seats with each other, the number of arrangements they can sit is
2!=2.
The total number of arrangements when AB and CD are always together will be 2×2×7!.
The number of sitting arrangements for the delegates when the delegates of the countries A and B are sitting together but the delegates of the countries C and B are not sitting together will be
=2×8!−2×2×7! = 60480

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