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

pokoljitef2

pokoljitef2

Answered

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?

Answer & Explanation

podesect

podesect

Expert

2022-06-26Added 20 answers

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 7 C 4 = 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 7 C 2 × 3 C 2 = 7 ! 2 ! × 5 ! × 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 7 C 2 × 3 C 2 + 7 C 3 × 3 C 1 + 7 C 4 .
= 7 ! 2 ! × 5 ! × 3 ! 2 ! × 1 ! + 7 ! 4 ! × 3 ! × 3 ! 2 ! × 1 ! + 7 ! 3 ! × 4 !
= 63 + 105 + 35 = 203

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?