Question 1202243
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A pond contains five catfish and six bluegill. 
If seven fish are caught at random, what's the probability that exactly three are catfish?
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<pre>
This probability is the ratio of two quantities.


The quantity in the denominator is the number of all septuplets from 5+6 = 11 fish,
which is the number of all combinations  {{{C[11]^7}}} = 330.


The quantity in the numerator is the product  {{{C[5]^3*C[6]^(7-3)}}} = {{{C[5]^3*C[6]^4}}} = 10*15 = 150.

It is the number of all septuplets that consist of 3 catfish and 7-3 = 4 bluegill.



The final probability is  {{{favored/total}}} = {{{150/330}}} = {{{5/11}}}.    <U>ANSWER</U>
</pre>

Solved, with complete explanations.



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<U>Comment from student</U> : Thank you for the answer and more importantly the explanation! I was missing 
the bluegill combination in the numerator, and I see why now. Much appreciated.



<U>My response</U> : &nbsp;&nbsp;As I see your reaction/comment, &nbsp;showing your interest to the subject, &nbsp;I can recommend you to look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in this site, &nbsp;where you will find many other similar &nbsp;(and different) &nbsp;problems solved.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Learn the entire subject from there &nbsp;(&nbsp;!&nbsp;)



Happy learning &nbsp;(&nbsp;!&nbsp;)



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