I struggle with this simple probability exercise. In a lake, there are 3 types of fishes A, B and C. The probability of catching one fish of type A is $p_A=0.6$, the probability of catching a fish of type B is $p_B=0.3$ and the probability of catching a fish of type C is $p_C=0.1$. We catch 7 fishes, what is the probability of the having 2 fishes of type A, 3 fishes of type B and 2 fishes of type C.
Thank you for your answer.
The probability of the sequence $AABBBCC$ is simply $0.6^20.3^30.1^2$. Now the number of such sequences is $\binom{7}{2} \binom{5}{3}$. Hence the desired probability is given by $\binom{7}{2} \binom{5}{3}0.6^20.3^30.1^2$.