A small pond contains nine catfish and two bluegill. If nine fish are caught at random, what is the probability that all of them are catfish?

Answer:

63/3465

Step-by-step explanation:

A small pond contains nine catfish and two bluegill.

Total number of fish = 9 catfish + 2 blue hill

= 11 fishes

Probability of picking one catfish = P(C) = P(9/11)

Probability of picking one bluegill = P(B) = P(2/11)

If nine fish are caught at random, the probability that all of them are catfish is calculated as:

= P(9 Catfish) = 9/11 × 8/10 × 7/9 × 6/8 × 5/7 × 4/6 × 3/5 × 2/4 × 1/3

= 362880/19958400

Further simplifying to the simplest fraction:

= 189/10395

= 63/3465

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