A box contains tickets marked 1,2,...,n. A ticked is drawn at random from the box. Then this ticket is replaced in the box and a second ticket is drawn at random. Find the probabilities of the following events:

a) The first ticket drawn is number 1 and the second ticket is number 2;

b) The numbers on the two tickets are consecutive integers, meaning the first number drawn is one less than the second number drawn.

c) The second number drawn is bigger than the first number drawn.

I can work out part a):

P(first ticket drawn is number 1 $\displaystyle \cap $ 2nd ticket drawn is number 2) = $\displaystyle \frac{1}{n} \times \frac{1}{n} = \frac{1}{n^2} $ but I am having trouble working out b) and c); the answers to which respectively are $\displaystyle \frac{n-1}{n^2} $ and $\displaystyle \frac{1-\frac{1}{n}}{2} $.

Any help would be appreciated .