Question

$21$ people 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?

• A. $20!$
• B. $2·18!$
• C. $18!$
• D. none of these

Answer 1

The correct option is B

$2·18!$

Explanation for the correct option:

From the question, Total number of people in party is $21$

Since, already two particular person seated either side of the host,

So, Remainder number of people is $21-2=19$

Therefore, Total number of ways to seat in these two seats is $2!=2\times 1=2$

The number of ways to arrangement of $n$element in a circular table is $(n-1)!$

Therefore, Number of ways to arrangement of $19$ people is $(19-1)!=18!$

Thus, Total number of ways $=2\times 18!$

So, correct answer is option $\left(B\right)$