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(B) Step $1$: Select $4$ students out of $8$ to be arranged around a table. The number of ways to select them is $^{8}C_{4} = \frac{8 	imes 7 	imes

Vedclass · Accepted Answer

$10080$

Vedclass · Answer

(B) Step $1$: Select $4$ students out of $8$ to be arranged around a table. The number of ways to select them is $^{8}C_{4} = \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 70$.Step $2$: Arrange these $4$ students around a circular table. The number of circular arrangements is $(4-1)! = 3! = 6$.Step $3$: The remaining $4$ students are arranged in a row. The number of linear arrangements is $4! = 24$.Step $4$: The total number of arrangements is the product of these values: $70 	imes 6 	imes 24 = 420 	imes 24 = 10080$.

Out of $8$ students in a classroom,$4$ of them are chosen and they are arranged around a table. If the remaining $4$ are arranged in a row,then the total number of arrangements that can be made with those $8$ students is

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