Button Tin #2

A tin contains 6 brass buttons and 9 pearl buttons. You draw 4 buttons one at a time, uniformly at random and without replacement.

What is the probability that the colours of the first two buttons and the colours of the last two buttons agree as unordered pairs? For example, (brass, pearl, pearl, brass) and (pearl, pearl, pearl, pearl) both count, but (brass, brass, pearl, brass) does not. Give an exact fraction in lowest terms.