There are 2n guests at a dinner party. Supposing that the 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. find the number of ways in which the company can be placed.

A number of 18 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 sitting arrangements can be made.

Eighteen guests have to be seated , half on each side of a ling 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 sitting arrangements can be made .

n different toys have to be distributed among n children. Find the number of ways in which these toys can be distributed so that exactly one child gets no toy.

A person invites a group of 10 friends at dinner and sits (i) 5 on a round table and 5 on other round table (ii) 4 on one round table 6 on other round table . Find no. of ways in each case in which he can arrange the guest?

A person is permitted to selected at least one and at most n coins from a collection of (2n+1) distinct coins. If the total number of ways in which he can select coins is 255, find the value of ndot

There are 15 points in a plane of which 4 points lie in one stright line and another 5 points lie in another straight line . The two lines are parallel and no three of the remaining 6 points are collinear . Find (a) the number of straight lines and (b) the number of trangles that can be formed by joining the 15 points .

A student is allowed to select at most n books from a collection of (2n + 1) books. If the total number of ways in which he can select at least one book is 63, find the value of n.

Direction : These question have statement I and statement II. Of the four choices given below choose the one that best describes the two statements. Statement I: The depletion of thermal layer is also generated at the junction of a p-n junction diode without any applied biasing. Statement II. The diffusion of thermal electrons and holes takes place from one region to another.

The distance between two places is 200 km. The time taken by moter car to travel from one place to another is more by 2 hrs than the time taken by a zeep car.If the speed of the motor car is 5 kms/hr less than the speed of the zeep car, then find the speed of the motor car.

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is^(2n)C_n-1.