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  • Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

Answers (1)

Let the women choose the chairs from amongst the chairs numbered 1 to 4.   

Two women can be arranged in 4 chairs in ^4P_2 ways

  In remaining 6 chairs, 3 men can be arranged in ^6P_3ways  

Total possible arrangements= 4_{\mathrm{p}_{2}} * 6_{\mathrm{p}_{3}}=\frac{4 !}{2 !} * \frac{6 !}{3 !}=1440

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infoexpert21

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