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Question
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.
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Solution
We have 2 women and 3 men
First women choose the chairs amongst the chairs 1 to 4
i.e. Total number of chairs = 4
So, the number of arrangements = 4P2 ways
Now 3 men choose from the remaining 6 chairs
So, the number of arrangements = 6P3 ways
∴ Total number of arrangements = 4P2 × 6P3
= `(4!)/((4 - 2)!) xx (6!)/((6 - 3)!)`
= `(4!)/(2!) xx (6!)/(3!)`
= `(4*3*2!)/(2!) xx (6*5*4*3!)/(3!)`
= 12 × 120
= 1440
Hence, the total number of possible arrangements are 1440.
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