Problem 1 (60 points): (a-d) 15pts a) You and two of your friends (say A and B) decided to join the selections of the universtiy chess team of QU. When you arrive to the venue of the selection event, you noticed that there are already 15 students arrived before you. The selection committee start to randomly pick three students at a time for evaluation. What is the probability that you and your friends will be selected at the first batch (order is not important)? b) Now repeat (a) if order is important, e.g., first you are selected, then friend A and then friend B. c) Assume that you are trying to hack a password and someone told you that the password contains two "A", one "B", three "3", and one "1". What is the probability that the password is "AAB1333"? d) Your brother bought the letter magnets as shown below. He was ordering them with his eyes closed. What is the probability that he will manage to write the word "BASKETBALL" in his first attempt? T B L A AB S