SOLUTION: 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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Question 1202243: A pond contains five catfish and six bluegill. If seven fish are caught at random, what's the probability that exactly three are catfish?
Answer by ikleyn(52776) About Me  (Show Source):
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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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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%5B11%5D%5E7 = 330.


The quantity in the numerator is the product  C%5B5%5D%5E3%2AC%5B6%5D%5E%287-3%29 = C%5B5%5D%5E3%2AC%5B6%5D%5E4 = 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%2Ftotal = 150%2F330 = 5%2F11.    ANSWER

Solved, with complete explanations.


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Comment from student : 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.


My response :   As I see your reaction/comment,  showing your interest to the subject,  I can recommend you to look into the lesson
                            - Elementary Probability problems related to combinations
                        in this site,  where you will find many other similar  (and different)  problems solved.

                        Learn the entire subject from there  ( ! )


Happy learning  ( ! )


When you will need to learn another/next subject, come again and ask  ( ! )