SOLUTION: in a shipment of 12 television sets 3 found out to be defective.In how many ways can a person take 5 sets which contains atleast 2 defective items.

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Question 353553: in a shipment of 12 television sets 3 found out to be defective.In how many ways can a person take 5 sets which contains atleast 2 defective items.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
There are "12 choose 5" or 12C5 ways to select any 5 TV sets.

From this number we must subtract: 

(1). the number of selections of 5 that contain no defective TV sets 

as well as 

(2). the number of selections of 5 that contain only 1 defective TV set.

We calculate (1) and (2)

(1). Choices of 5 with no defective TV sets:

     Since there are 12 sets and 3 are defective, there are 12-3 or 9
     non-defective ones, so this is "9 choose 5", or 9C5.

(2). Choices of 5 with 4 non-defective sets and 1 defective set:

     "9 choose 4" times "3 Choose 1" or (9C4)(3C1)

Subtracting the number of choices of (1) and (2), which do not contain 
at least 2 defective TVs from the total number of choices of any 5
TVs, we have:

12C5 - 9C5 - (9C4)(3C1)

 792 - 126 - (126)(3) = 288

That's the answer, 288.

Edwin
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