Ten chairs are evenly spaced around a round table and numbered clockwise from $1$ through $10$ . Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How many seating arrangements are possible?

240

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360

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480

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540

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720

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Solution

The correct option is B $480$
Let us first seat $1$ of men.
There are $10$ possible seats. Since men and women are to seated alternately the subsequently men will have $4, 3, 2, 1$ choices for the first wife and only $1$ choice for subsequent women.
$∴$ Total $= 10 \times 4 \times 3 \times 2 \times 1 \times 2$
$= 480.$
Hence, the answer is $480.$

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Ten chairs are evenly spaced around a round table and numbered clockwise from 1 through 10. Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How many seating arrangements are possible?

The correct option is B 480Let us first seat 1 of men.There are 10 possible seats. Since men and women are to seated alternately the subsequently men will have 4,3,2,1 choices for the first wife and only 1 choice for subsequent women.∴ Total =10×4×3×2×1×2 =480.Hence, the answer is 480.

Ten chairs are evenly spaced around a round table and numbered clockwise from $1$ through $10$ . Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How many seating arrangements are possible?