In an examination, a question paper has 12 questions divided into Part I and Part II containing 5 and 7 questions. A student must attempt 8 questions, selecting at least 3 from each part. Number of ways?

The number of ways in which 12 identical pens can be distributed between two students, if each student is to get at least two pens, is

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

A triangle PQR is such that 3 points lie on the side PQ, 4 points on QR and 5 points on RP respectively. Triangles are constructed using these points as vertices. What is the number of triangles so f…