Independent and dependent events
Multiply the two probabilities, and if the first item is not replaced, drop both the top and bottom of the second fraction.
A worked example
From a bag of 8 counters of which 5 are red, drawing two reds without replacement is (5/8) x (4/7) = 20/56, which is 5/14.
The mistake people actually make
It is easy to take one off the total but forget to take one off the favourable count as well. Both change when the item is kept.