In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

In an examination, Yamini has to select 4 questions from each part. There are 6, 7 and 8 questions is Part I, Part II and Part III respectively. What is the number of possible combinations in which she can choose the questions?

In how many ways can 12 things be equally divided among 4 persons?

If p(n) is the statement "12n + 3" is a multiple of 5, then show that P (3) is false, whereas P(6) is true.

Let p(n) be the statement "n² + n is even". If P(k) is true, then show that P(k+1) is true.