HW HELP: Thank you!! Please show work

Using your knowledge of the Binomial Theorem, provide the correct answers to the following problems and questions. Make sure to completely answer each problem or question and show all of your work. (2 points each) 1. Using your own worked out example, explain how to use binomial coefficients and the Binomial Theorem to expand a binomial. 2. You are taking a test consisting of 20 multiple-choice questions. For each question, there are 4 choices (i.e., A, B, C, D). If you guess randomly on 15 of the questions, what is the probability you will answer 10 of them correctly? 3. According to a 2010 report by the National Center for Health Statistics, a unit of the U.S. Department of Health and Human Services, 11.5% of adults in the United States suffer from heart disease. If 8 adults are selected at random, what is the probability 3 of them will suffer from heart disease? (Hint: Use the reported percentage of heart disease incidence as the probability of the event occurring.)