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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 = 330.
The quantity in the numerator is the product = = 10*15 = 150.
It is the number of all septuplets that consist of 3 catfish and 7-3 = 4 bluegill.
The final probability is = = . 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 ( ! )