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 ?

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

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?

20 % of 25 students in a class are boys.How many girls are in the class?

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?

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 class has 30 students, In how many ways can three prizes be awarded so that: no student gets more than one prize?

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 ?

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?