In a lot of 12 microwave ovens, there are3 defective units. A person has to ordered 4 of these units and since each is identically packed, the selection will be random. What is he probability that( i) all are good (ii)exactly 3 units are good (iii) at least 2 units are good.

As there are 12 microwave oven in total, so choosing 4 out of 12 is ¹²C₄
1) all are good, so chose four out of good microwave oven = ⁹C₄
Hence the probability = ⁹C₄ /¹²C₄

2) Exactly three units are good, it means choosing three from 9 and and one from defective lot of three.
So ⁹C₃ * ³C₁
Hence the probability = ⁹C₃ * ³C₁ / ¹²C₄

3) Atleast two units are good means : two good and two defective  + three good and one defective + all four good
So the number of ways are ⁹C₂*³C₂ + ⁹C₃*³C₁ + ⁹C₄
Hence the probability = ( ⁹C₂*³C₂ + ⁹C₃*³C₁ + ⁹C₄) /¹²C₄