Roorkee University has to send 10 professors to 5 centers for its entrance examination, 2 to each center. Two of the enters are in Roorkee and the others are outside. Two of the professors prefer to work in Roorkee while three prefer to work outside. In how many ways can this be made if the preferences are to be satisfied?

A firm of Chartered Accountants in Bombay has to send 10 clerks to 5 different companies, two clerks in each. Two of the companies are in Bombay and the others are outside. Two of the clerks prefer to work in Bombay while three others prefer to work outside. In how many ways can the assignment be made if the preferences are to be satisfied.

There are two works each of 3volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?

A library has two books each having three copies and three other books each having tow copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separated.

Kartar goes to a movie. The cinema hall has two entrances and three exits. In how many ways can Kartar enter and exit from the hall ?

There are two works each of 3volumes and two works each of 2 volumes; In how many ways can be 10 books be placed on a shelf so that the volumes of the same work are not separated

In an examination hall there are four rows of chairs. Each row has 8 chairs one behind the other. There are two classes sitting for the examination with 16 students in each class. It is desired that i each row, all students belong to the same class and that no two adjacent row are allotted to the same class. In how many ways can these 32 students be seated?

Gopi, Nithya, Shilpa, Renu, Gowtham, Priya, Prasanth and Sridhar are sitting around a square table in such a way that four of them sit at four corners of the square while four sit in the middle of each of the four sides. The ones who sit at the four corners face the center while those who sit in the middle of the sides face outside. Two females sit in the middle of the sides and two at the corners. Shilpa sits second to the left of Prasanth. Prasanth sits in the middle of one of the sides. Gopi sits fourth to the right of his wife and his wife is not an immediate neighbour of Shilpa or Prasanth. Nithya sits third to right of her husband. Nithya does not sit at any of the corners. Only Renu sits between Nithya and Sridhar. Sridhar is the husband of Shilpa. Gowtham is a male. How many people sit between Nithya and Gopi when counted in anti-clockwise direction from Nithya ?