A person invites 8 guests to a dinner and pla | vedclass

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(B) The number of ways to select $5$ persons out of $8$ is ${}^8C_5$.Now,the number of ways to arrange $5$ guests at a round table is $(5-1)! = 4!$.Th

Vedclass · Accepted Answer

$2688$

Vedclass · Answer

(B) The number of ways to select $5$ persons out of $8$ is ${}^8C_5$.Now,the number of ways to arrange $5$ guests at a round table is $(5-1)! = 4!$.The number of ways to arrange the remaining $3$ guests at another round table is $(3-1)! = 2!$.Thus,the total number of ways is ${}^8C_5 	imes 4! 	imes 2!$.Calculation: ${}^8C_5 = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$.Total ways $= 56 	imes 24 	imes 2 = 56 	imes 48 = 2688$.Hence,option $(B)$ is correct.

$A$ person invites $8$ guests to a dinner and places $5$ of them at one table and the remaining $3$ at another,both the tables being round. The number of ways in which the guests can be arranged is

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