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

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