A lucky-dip box at a school fete holds 4 green and 6 white tokens. A token is drawn, its colour noted, and it is dropped back into the box before the next draw. Three draws are made in this way. What is the probability that a green token turns up exactly twice?

Because the token goes back, every draw independently gives green with probability 4/10 = 2/5. Exactly two greens in three draws can happen in $C(3,2)=3$ orders (GGW, GWG, WGG), so the probability is $3\times (2/5{)}^2\times (3/5)=3\times 4/25\times 3/5=36/125$. Trap $12/125=(2/5{)}^2\times (3/5)$ prices only ONE of those three orders and forgets the $C$(3,2) factor. Trap $8/125=(2/5{)}^3$ is 'all three green'. Trap 44/125 adds that case in to give 'at least two green'.