SOLUTION: dear tutor, please help me with this question: there are 14 radar dishes, 8 work fine and 6 are defective. The system works as long as two defectives are not next to each other. Wh

Algebra ->  Probability-and-statistics -> SOLUTION: dear tutor, please help me with this question: there are 14 radar dishes, 8 work fine and 6 are defective. The system works as long as two defectives are not next to each other. Wh      Log On


   

Question 342306: dear tutor, please help me with this question: there are 14 radar dishes, 8 work fine and 6 are defective. The system works as long as two defectives are not next to each other. What is the probability that it will work? Please show your work.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
dear tutor, please help me with this question: there are 14 radar dishes, 8 work fine and 6 are defective. The system works as long as two defectives are not next to each other. What is the probability that it will work? Please show your work.
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# of ways to place the six defectives so the system will work.
Pattern: 11111111 : 8 good ones
There are 9 slots in which to place the defectives If one can be placed
on either end.
9C6 = 84 ways to place the 6 defectives so the system works
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Total number of ways to arrange the 14 radars = 14!
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P(it will work) = 84/14! = 0.00000000096354..
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Cheers,
Stan H.