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A tea paty is arranged for 16 people along two sides of a long table with 8 chairs on either sides. Four men wish to sit on one side and 2 on other side. In how many ways they can be seated?

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Let both the sides be named $A\:and \:B$
Having seated the 4 men on side A and 2 on B, we are left with 10 persons.
We can choose 4 of them for side A in $^{10}C_4$ ways. and remaining 8
can be seated automatically on side B.
After selecting the persons for each side, arrangement is done.
On each side arrangement is done is $8!$ ways.
$\therefore$ The required no. of seating arrangements = $^{10}C_4.8!8!$
answered Aug 20, 2013 by rvidyagovindarajan_1

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