A box contains n n\,n red counters and 6 blue counters, where n n\,n is a positive integer. Two counters are taken from the box at random, without replacement.
The probability that both counters taken are blue is 18\displaystyle \frac{1}{8}81.
Show that n2+11n−210=0n^2 + 11n - 210 = 0n2+11n−210=0.
Hence find the value of nnn.
Find the probability that the two counters taken are different colours.