please answer 3-6

3. (6 points) What is the coefficient of x* in the expansion of (2x + 1) 6 4. (10 points) An admission test given by a university contains 12 true-false questions. Nine or more of the questions must be answered correctly in order to be admitted. a. How many different ways can the answer sheet be filled out? b. How many different ways can the answer sheet be filled out so that 9 or more questions are answered correctly? 5. (8 points) A woman is getting married. She has 16 best friends but can only select 6 of them to be her bridesmaids, one of which needs to be her maid of honor. How many ways can she do this if a. she first selects the 6 bridesmaids, and then selects one of them to be the maid of honor? b. if she first selects her maid of honor, and then 5 other bridesmaids? 6. (8 points) A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if a. a person can serve on any number of committees? b. no person can serve on more than one committee