probability picking parts no replacement

Question

In a bin containing 30 parts, 27 parts are good and 3 parts are defective.

a) What is the probability that if you select 3 parts randomly, without replacing the parts in the bin, from the bin that you will have 1 defective part?

I thought of $\dfrac{\dbinom{27}{1}\dbinom{26}{1}\dbinom{3}{1}}{\dbinom{30}{1}\dbinom{29}{1}\dbinom{28}{1}}$

Answer 1

Close, but as you seek the probability for obtaining $2$ from the $27$ good parts and $1$ from the $3$ defective parts, when selecting any $3$ from all $30$ parts (without replacement or bias), it is: $$\dfrac{\dbinom{27}{2}\dbinom{3}{1}}{\dbinom{30}{3}}$$.