12 guests at a dinner party are to be seated along a circular table. Supposing that the master and mistress of the house have fixed seats opposite one another, and that there are two specified guests who must always, be placed next to one another; the number of ways in which the company can be placed, is:
How I tried:
as the master and mistress are to be seated opposite to each other there are 2 possible ways (interchanging their position) of arrangement, now the two guests to be seated next to each other also have two possible ways (interchanging their position) now these two guests be treated as one guest and then arranging the 12-2-2+1=9 guests in remaining position= 9!
Therefore the total number of arrangement =2.2.9!=36.9!
But the answer is A)20.10!, where am I wrong, how to solve the problem?
. means multiply