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

The number of ways in which the letters of the word “ALGEBRA” can be arranged so that two A's are not adjacent, are

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…

If a cube is to be painted with red and blue colour in such a way that each face gets exactly one colour, then in how many ways this cube can be painted?

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?