Question 1185833: In a shipment of 22 smart phones, three are defective. How many ways can a quality control inspector randomly test six smart phones, of which three are defective?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! In a shipment of 22 smart phones, three are defective. How many ways can a quality control inspector randomly test six smart phones, of which three are defective?
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The 1st pick is 1 of 22, then 1 of 21, etc
---> 22*21*20*19*18*17 = 53721360
But, there are 6*5*4*3*2*1 = 720 ways to select the 6.
53721360/720 = 74613 ways
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Don't try this at home.
Answer by ikleyn(52900)  (Show Source):
You can put this solution on YOUR website! .
In a shipment of 22 smart phones, three are defective.
How many ways can a quality control inspector randomly test six smart phones,
of which three are defective?
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They want you calculate the number of different sextuplets (subsets of 6 smartphones)
that contain that three defective smartphones.
Then, it is obvious, that the number of such sextuplets is equal to the number of different TRIPLETS
that you can select from 22-3 = 19 good smartphones to add them to that unique triple of
defective smartphones.
Finally,  =  = 969 is your ANSWER.
Solved and thoroughly explained.
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