From probability to proving

Lots of questions that I've tried and gotten stuck on. I'll post the questions and my answers to them

1) Fully simplify $\displaystyle \frac{x^2-11x+28}{3x^2-10x-8}$

I got $\displaystyle \frac{(x-4)(x-7)}{(3x-4)(x+2)}$ I think that's right.

2) Nicolas has 30 beads in a bag. 9 of them are white. 8 green. 13 blue. What is the probability that if two beads are taken from the bag at random that they will not be the same colour. I got $\displaystyle \frac{113}{174}$ Definitely wrong

3)OPR is a triangle. $\displaystyle \longrightarrow$ OP = p and $\displaystyle \longrightarrow$OR = r

a.Find the vector $\displaystyle \longrightarrow$PR in terms of p and r

(No answer, I tried it but I just got stuck)

A os a point on PR such that PA:AR=7:2

b. Show that $\displaystyle \longrightarrow$OA = $\displaystyle \frac{1}{9}(2p+7r)$

Again I tried but couldn't even get close to an answer...

4)Prove that, for all positive integer values of n, $\displaystyle (7n+1)^2-(7n-1)^2$ is a multiple of 2.

Here I found out why but I just don't know how to word it so an exam will accept it...