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It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
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According to the problem women will sit at the even places $(2,4,6$ and 8$)$
They can be seated in $\mathrm{P}(4,4)=4 !=24$ ways
Men will sit on the odd seats (i.e., 1,3, 5, 7 and 9)
They can sit on these seats in $\mathrm{P}(5,5)=5 !=120$ ways
If total no. of ways is $\mathrm{P}$ then, $\mathrm{P}=24 \times 120=2880$
They can be seated in $\mathrm{P}(4,4)=4 !=24$ ways
Men will sit on the odd seats (i.e., 1,3, 5, 7 and 9)
They can sit on these seats in $\mathrm{P}(5,5)=5 !=120$ ways
If total no. of ways is $\mathrm{P}$ then, $\mathrm{P}=24 \times 120=2880$
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