True or False:
Eighteen guests are 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 of the table. The number of ways in which the seating arrangements can be made is `(lfloor11)/(lfloor5lfloor6)(lfloor9)^2`

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?

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 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

If 20 persons were invited for a party, in how many ways can they and the host be seated at a circular table? In how many of these ways will two particular persons be seated on either side of the host?

he number of ways in which 5 boys and 5 girls can be seated for a photograph so that no two girls sit next to each other is :

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?

As shown in the given figure. the two sides of a step ladder BA and CA are 1.6 m long and hinged at A.A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1,2 m from B along the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in te rope and forces exerted by the floor on the ladder. (Take g = 9.8 ms^-2 ) (Hint: consider the equilibrium of each side of the ladder separately).

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (4, 3).

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (3, 4).