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 _________.

The number of ways to arrange 'n' distinct entities in a circular table = (n-1)!

Now, the number of ways in which Mr and Mrs Sharma (1 entity) and 4 persons along with Mr and Mrs Ahuja (4+2=6 entities) can sit together in the round table is = $$6!\cdot2!$$

(Since there are 1+6=7 entities, no. of ways of arranging them are (7-1)!=6! ways

Also, Mr and Mrs Sharma can be arranged in 2! ways)

But in these arrangements, there are cases in which Mr and Mrs Ahuja are also together. We need to eliminate such cases.

Now, the number of ways in which Mr and Mrs Sharma (1 entity), Mr and Mrs Ahuja (1 entity) and 4 persons (4 entities) can sit together in the round table are = $$5!\cdot2!\cdot2!$$

(Since there are 6 entities, no. of ways of arranging them is 5! ways

Also, Mr and Mrs Sharma can be arranged in 2! ways, and Mr and Mrs Ahuja can be arranged in 2! ways)

So, total number of seating arrangements = $$6!\cdot2!-5!\cdot2!\cdot2!=5!(6\cdot2-2\cdot2)=5!(12-4)=120\times\ 8=960$$ ways