Question

20 persons are invited for a party. The different number of ways in which they can be seated at a circular table with two particular person seated on either side of the host is:

• A. $19!2!$
• B. $18!2!$
• C. $20!2!$
• D. $18!3!$

Answer 1

Answer: (B)

$18!2!$

Total number of persons in party$=21$
As two persons A and B are to be seated besides the host H, number of arrangements are AHB and BHA.
Taking {A,H,B} as a single element.
$no$ of persons$=19$
$\therefore no$ of arrangements$=(n-1)!$
$=18!$
$\therefore$Total $no$ of ways$=18!\times 2$ways of arrangement besides host
$=18!\times 2$