As requested by Lucas:the sock question

Here is part of the tree diagram.



Clue: This question is a no-replacement question.

e.g. Find the probability that he takes 2 black socks.

That will be he get a black sock, then another black sock.
Hence P(B and B) = 2/10 x 1/9 = 1/45 (after he takes out 1 black, there is only 1 blakc left and a total of 9 socks.)

Hope this is helpful.