There are N counters in a bag, 4 being red and the rest being blue. I take two counters at random from the bag (without replacing the first).The chance i take two blue counters is 1/3, See below in the answer box

Show that n^2-13n+30=0We note that 4/N denotes the probability of a me picking a red counter and (N-4)/N denotes the chance of me picking a blue counter.Since I select two counters and do not replace the first counter, it follows that the chance of me selecting two blue counters isN-4/N * N-5/N-1 and using the information from the question, this is equal to 1/3. We then rearrange N to get the required form.