A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular and two on the other side. In how many ways can they be seated?

Answer

`.^(8)P_(4)xx.^(8)P_(2)xx10!`

Explanation

There are 8 chairs on each side of the table. Let sides be represented by A and B. let four persons sit on side A, then number of ways arranging 4 persons on 8 chairs on side `A=.^(8)P_(4)` and then two persons sit on side B, then number of ways arranging 2 persons on 8 chairs on side `B=.^(8)P_(2)` and arranging the remaining 10 persons in remaining 10 chairs in 10! ways.
hence, the total number of ways in which the persons can be arranged`=.^(8)P_(4)xx.^(8)P_(2)xx10!=(8!*8!*10!)/(4!6!)`