A test with multiple choice questions consists of twelve questions with 4 possible answers each. In each question only one answer is correct. A student answers all questions. i). Calculate the ways in which the test can be answered. ii). Calculate the ways in which it is possible to answer the test so that exactly 8 answers to be correct. iii). To receive a scholarship a Student's must answer more than 10 correctly questions. If the Student answers all the questions in a random way, write an expression about the possibility for the Student to receive a scholarship (it is not required to be done the act). a iv). What is the number of expected correct answers of the student and what is the standard deviation of the number of correct answers?