From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen ?

From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done ?

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made ?

A man has 7 friends. In how many ways can he invite one or more of them to a party ?

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made ?

A man has 10 friends. In how many ways he can invite one or more of them to a party?

There are 25 students in a class in which 15 boys and 10 girls. The class teacher select either a boy or girl for monitor of the class. In how many ways the class teacher can make this selection?

A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted ?

A Student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 questions in part B, in how many ways can the student choose 10 questions?

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 in each row, all students belong to the same class and that no two adjacent rows are allotted to the same class. In how many ways can these 32 students be seated?

There are 100 students in a hostel. Food provision for them is for 20 days. How long will these provisions last, if 25 more students join the group?