A jar on a Nagpur sweet shop counter holds 7 mango candies and 5 orange candies, identical to the touch. A child scoops out 3 candies together. What is the probability that exactly two of them are mango?

Total scoops = $C(12,3)=220$. Exactly two mango means 2 mango and 1 orange: $C(7,2)\times C(5,1)=21\times 5=105$. Probability = 105/220 = 21/44. Trap $7/44=C(7,3)/220$ answers 'all three mango'. Trap 7/11 = 140/220 adds the all-mango case to give 'at least two mango' — 'exactly' forbids that. Trap $7/22=C(5,2)\times C(7,1)/220$ swaps the two colours.