Question 1195012
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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 

    {{{C[15]^5}}} = {{{15!/(5!*10!)}}} = {{{(15*14*13*12*11)/(1*2*3*4*5)}}} = 3003.


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

    {{{C[6]^3*C[9]^2}}} = 20*36 = 720.


Therefore, the sough probability is  

    P = {{{favorable/total}}} = {{{720/3003}}} = {{{240/1001}}} = 0.23976  (rounded).    <U>ANSWER</U>
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Solved.