An urn contains 7 red balls, 6 green balls, and 9 yellow balls. Ten balls are chosen without replacement. What is the probability that the 3rd ball chosen was green, given that the 5th ball chosen was yellow?

Since "without replacement" implies exchangeability, this problem can be simplified to

P(x₁: Yellow and x₂: Green)\(P(x₁:Yellow))

Can someone show the details of the calculation to compute this probability?