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(A) There are $4$ rows of chairs (let us label them $I, II, III, IV$),each consisting of $8$ chairs. It is required that all students in a single row

Vedclass · Accepted Answer

$2 	imes 16! 	imes 16!$

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(A) There are $4$ rows of chairs (let us label them $I, II, III, IV$),each consisting of $8$ chairs. It is required that all students in a single row belong to the same class and no two adjacent rows are assigned to the same class.Since there are $2$ classes (let us call them $C_1$ and $C_2$),the rows must be assigned in an alternating pattern. The two possible patterns for the classes are:Pattern $1$: Row $I$ $(C_1)$,Row $II$ $(C_2)$,Row $III$ $(C_1)$,Row $IV$ $(C_2)$.Pattern $2$: Row $I$ $(C_2)$,Row $II$ $(C_1)$,Row $III$ $(C_2)$,Row $IV$ $(C_1)$.Thus,there are $2$ ways to assign the classes to the rows.For each class,there are $16$ students who must be arranged in the $16$ chairs assigned to that class. The number of ways to arrange $16$ students in $16$ chairs is $16!$.Since both classes have $16$ students,the total number of ways to seat them is $2 	imes 16! 	imes 16!$.

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