1. Three married couples are going to the movies. (a) In how many ways can the six people stand in line at the ticket booth, assuming the couples don't need to stay together? (b) In how many ways can they stand in line at the ticket booth if couples must stay together?

2. (a) A test has two sections of five questions each. The instructions say to answer three questions in each section. In how many ways can a student choose the questions to complete the exam?

(b) Another test has three sections of four questions each. According to the instructions, the student must answer two questions from each of any two sections and one question from the other section. In how many ways can the student choose questions to answer?