Ways to select 4 children out of 6 girls and 4 boys with at least 1 girl -

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?

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?

How many ways a captain and a vice-captain can be selected from a team of 11 players?

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

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 w…