A box contains n n\,n petrol key fobs and 6 diesel key fobs, where n n\,n is a positive integer. A fob is selected at random, replaced, and then a second fob is selected.
The probability that both fobs selected are diesel is 14\displaystyle \frac{1}{4}41.
Show that n2+12n−108=0n^2 + 12n - 108 = 0n2+12n−108=0.
Hence find the value of nnn.
Find the probability that the two fobs taken are of different types.