Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements is _________.
Explanation:
Let us form a group X of Mr. and Mr. Ahuja. They can be arranged in 2! = 2 ways.
Now, X and 4 other persons can be seated around a circle in 4! = 24 ways.
Now we have total 5 people (X is counted as 1 only, no one should sit between Ahujaas) and there are 5 places between these 5 people for Mr. and Mrs. Sharma to sit.
We need to select 2 of these 5 places for Mr. and Mrs. Sharma. This can be done in 5C2 = 10 ways. Mr. and Mrs. Sharam can sit in these 2 places in 2! = 2 ways.
∴ Total number of ways = 2 × 24 × 10 × 2 = 960.
Hence, 960.
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