Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?

There are 12 different books in a shelf. In how many ways we can select atleast one of them?

From among the 36 teachers in a school, one principal and one vice principal are to be appointed. In how many ways can this be done?

There are 3 candidates for a classical, 5 for a Mathematical,, and 4 for a Natural science scholarship. In how many ways can these scholarships be awarded? In how many ways one of these scholarships be awarded?

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.

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.

Six X 's have to be placed in the squares of the figure below, such that each row contains atleast one X. in how many different ways can this be done?

There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?

There are 4 students for physics, 6 students for chemistry and 7 students of mathematics gold medal. In how many ways one of these gold medals be awarded?

A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone (a) 35 (c) 60 (b) 48 (d) 22

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?