Eighteen guests have to be Seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the Seating arrangements can be made.

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?

Seven perons are to be seated in a row. The probability that two particular persons sit next to each other is:

Six candidates are called for interview to fill four posts in an office. Assuming that each candidate is fit for each post. determine the number of ways in which : first three posts can be filled.

There are 2n guests at a dinner party. Supposing that eh master and mistress of the house have fixed seats opposite one another and that there are two specified guests who must not be placed next to one another, show that the number of ways in which the company can be placed is (2n-2!)xx(4n^2-6n+4)dot

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated ? Find also the number of ways of their seating if all the ladies sit together.

In how many ways can 15 members of a council sit along a circular table, when the secretary is to sit on one side of the chairman and the deputy secretary on the other side?

There are n numbered seats around a round table. Total number of ways in which n_(1)(n_(1) lt n) persons can sit around the round table, is equal to

A current of 10 A is flowing in a long straight wire situated near a rectangular circuit whose two sides oflength 0.2m are parallel to the wire. One of them is at a distance of0.05m and the other at a distance of 0. IOm from the wire. The wire is in the plane of the rectangle. Find the magnetic flux through the rectangular circuit. If the current decays uniformly to zero in 0.02s, fmd the EMF induced in the circuit and indicate the direction in which the induced current flows.

A family consists of a grandfather, 5 sons and daughters and 8 grand child. They are to be seated in a row for dinner. The grand children wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?