A shipment of 10 microwaves contains 3 defective units. In how many ways can a...

Step 1
Out of 10 units of microwave there are 7 good units and 3 defective units.
(a)The number ways of receiving all 4 units perchased by the vending company to be good ones are ${\displaystyle {}^7{C}_4=\frac{7!}{3!\times 4!}=35}$
Step 2
(b)The number ways of receiving 2 good units out of 4 units perchased by the vending company are ${\displaystyle {}^7{C}_2\times {}^3{C}_2=\frac{7!}{2!\times 5!}\times \frac{3!}{2!\times 1!}=63}$.
Step 3
(c)The number ways of receiving at least 2 good units out of 4 units perchased by the vending company are ${\displaystyle {}^7{C}_2\times {}^3{C}_2+{}^7{C}_3\times {}^3{C}_1+{}^7{C}_4}$.
${\displaystyle =\frac{7!}{2!\times 5!}\times \frac{3!}{2!\times 1!}+\frac{7!}{4!\times 3!}\times \frac{3!}{2!\times 1!}+\frac{7!}{3!\times 4!}}$
${\displaystyle =63+105+35=203}$