pokoljitef2

2022-06-25

A shipment of 10 microwaves contains 3 defective units. In how many ways can a vending company purchase 4 of these units and receive (a) all good units (b) two good units and (c) at least two good units?

podesect

Expert

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 ${\text{}}^{7}{C}_{4}=\frac{7!}{3!×4!}=35$
Step 2
(b)The number ways of receiving 2 good units out of 4 units perchased by the vending company are ${\text{}}^{7}{C}_{2}×{\text{}}^{3}{C}_{2}=\frac{7!}{2!×5!}×\frac{3!}{2!×1!}=63$.
Step 3
(c)The number ways of receiving at least 2 good units out of 4 units perchased by the vending company are ${\text{}}^{7}{C}_{2}×{\text{}}^{3}{C}_{2}+{\text{}}^{7}{C}_{3}×{\text{}}^{3}{C}_{1}+{\text{}}^{7}{C}_{4}$.
$=\frac{7!}{2!×5!}×\frac{3!}{2!×1!}+\frac{7!}{4!×3!}×\frac{3!}{2!×1!}+\frac{7!}{3!×4!}$
$=63+105+35=203$

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