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20 persons are invited for a party. In how many different ways can they and the host be seated at a circular table, if the two particular persons are to be seated on either side of the host
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$2.18 !$
There are $20+1=21$ persons in all. The two particular persons and the host be taken as one unit so that these remain $21-3+1=$ 19 persons to be arranged in 18 ! ways. But the two person on either side of the host can themselves be arranged in 2! ways. Hence there are $2!18!$ ways or $2.18!$ ways.
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