SOLUTION: There are 15 glass vases sold in an antique shop and 6 of them are slightly cracked. What is the chance that when a customer buys 5 vases 3 of them will be cracked?

Question 1195012: There are 15 glass vases sold in an antique shop and 6 of them are slightly cracked. What is the chance that when a customer buys 5 vases 3 of them will be cracked?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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There are 15 glass vases sold in an antique shop and 6 of them are slightly cracked.
What is the chance that when a customer buys 5 vases 3 of them will be cracked?
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Of 15 glass vases, 6 are cracked and 15-6 = 9 are not.


To answer the question, we should calculate the number of all possible 5-vase subsets 
in the set of 15 vases, and then relate it to the number of all possible subsets
of 5 vases, comprising of 3 cracked and 2 good vases.


The number of all possible 5-vase subsets in the set of 15 vases is 

     =  =  = 3003.


The number of all possible 5-vase subsets comprising of 3 cracked and 2 good vases is

     = 20*36 = 720.


Therefore, the sough probability is  

    P =  =  =  = 0.23976  (rounded).    ANSWER

Solved.

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