A couple can sit with 6 guests around a circu | vedclass

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(A) Treat the couple as a single unit. Now,we have $1$ unit (the couple) and $6$ guests,making a total of $7$ entities to be arranged around a circula

Vedclass · Accepted Answer

$1440$

Vedclass · Answer

(A) Treat the couple as a single unit. Now,we have $1$ unit (the couple) and $6$ guests,making a total of $7$ entities to be arranged around a circular table.Number of ways to arrange $n$ items in a circle is $(n-1)!$.So,the number of ways to arrange these $7$ entities is $(7-1)! = 6! = 720$.Within the couple unit,the $2$ individuals can arrange themselves in $2! = 2$ ways.Therefore,the total number of ways is $6! 	imes 2! = 720 	imes 2 = 1440$.

$A$ couple can sit with $6$ guests around a circular table. In how many ways can they sit if the couple sits in consecutive seats?

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