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.

^{12}C

_{4}

1) all are good, so chose four out of good microwave oven =

^{9}C

_{4}

Hence the probability =

^{9}C

_{4}/

^{12}C

_{4}

2) Exactly three units are good, it means choosing three from 9 and and one from defective lot of three.

So

^{9}C

_{3}*

^{3}C

_{1}

Hence the probability =

^{9}C

_{3}*

^{3}C

_{1}

_{ }/

^{12}C

_{4}

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

^{9}C

_{2}*

^{3}C

_{2}+

^{9}C

_{3}*

^{3}C

_{1}+

^{9}C

_{4}

Hence the probability = (

^{9}C

_{2}*

^{3}C

_{2}+

^{9}C

_{3}*

^{3}C

_{1}+

^{9}C

_{4}) /

^{12}C

_{4}

**
**