Eight chairs are numbered 1 to 8. Two women a | vedclass

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(D) Step $1$: The two women choose their chairs from the chairs marked $1$ to $4$. Since the order in which they sit matters (as chairs are distinct),

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None of these

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(D) Step $1$: The two women choose their chairs from the chairs marked $1$ to $4$. Since the order in which they sit matters (as chairs are distinct),the number of ways is $^4P_2 = 4 	imes 3 = 12$.Step $2$: After the women have occupied $2$ chairs,there are $8 - 2 = 6$ chairs remaining in total.Step $3$: The three men then choose their chairs from the remaining $6$ chairs. The number of ways is $^6P_3 = 6 	imes 5 	imes 4 = 120$.Step $4$: The total number of arrangements is the product of these two steps: $^4P_2 	imes ^6P_3 = 12 	imes 120 = 1440$.Since $1440$ is not listed in options $A, B,$ or $C$,the correct answer is $D$.

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose the chairs from amongst the chairs marked $1$ to $4$,and then men select the chairs from amongst the remaining. The number of possible arrangements is

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