Combinations problem - Finding the number I would like to ask for your confirmation to my thought in regards with the following exercise:
One man has 30 different statues, 27 genuine and 3 fake. He sold 10 of these statues in museum A, 10 in museum B and 10 in museum C. What is the probability that each of these museums bought fake statue from the man?
I found the probability for each museum, through combinations, that is :
$$
\frac{{3 \choose 1} {27 \choose 9}+{3 \choose 2 } {27 \choose 8}+{3 \choose 3} {27 \choose 7}}{{30 \choose 10}}
$$
Is my way of thinking correct?
Thank you very much in advance.

Another answer (related to Parcly's): Imagine each museum has 10 tables, one for each statue it bought. The first fake occupies one of these tables. The next fake is equally likely to occupy each of the remaining 29 tables, so the probability that it's in a different museum from the first fake is $\frac{20}{29}$. In this event, of the 28 remaining tables, 10 are in the last museum, so the probability that the last fake is in a different museum from both of the first two fakes (given that the first two are in different museums) is $\frac{10}{28}$. The probability that this all happens is therefore $\frac{20}{29}\frac{10}{28}=\frac{50}{203}$.
