Question 1183758
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A batch of pills consist of 10 good pills and 4 that are defective (contain the wrong amount of the drug). 
If 5 pills are randomly selected without replacement, what is the probability that all 4 of the defective pills are selected?
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            I do not agree with the solution by @Boreal.

            My solution and my answer are different.



<pre>
The number of all possible subsets of 5 pills, randomply selected from the total set of 10+4 = 14 pills is

    {{{C[14]^5}}} = {{{(14*13*12*11*10)/(1*2*3*4*5)}}} = 2002.


It is the cardinality of the total space of events.


The number of all possible subsets of 5 pills, containing 4 defective pills (and, hence, one good pill), is 10.

These subsets contain all 4 defective pills and one of 10 good pills, so the cardinality of this set 
("favorable" set of events) is 10.


The probability under the problem's question is thus


    P = {{{favorable/total}}} = {{{10/2002}}} = {{{5/1001}}} = 0.004995  (rounded).    <U>ANSWER</U>


If you want a general formula, here it is  P = {{{(C[4]^4*C[10]^1)/C[14]^5}}}.
</pre>

Solved and explained.