1. (50 pts) For the following problems, consider a group of 50 students. There are 8 Computer Engineering (CE) majors, 12 Computer Science (CS) majors, 20 Electrical Engineering (EE) majors, and 10 Software Engineering (SE) majors. There are no dual major students. (a) (15 pts) Select 7 of the 50 students and line them up from left to right. How many ways can this be done when we consider their individual names, not their majors? Note that the "left to right" order matters, e.g, ABC is different as BAC. (b) (15 pts) Select 5 of the 50 students and line them up from left to right. How many ways can this be done if we consider only their majors, and not their names? (c) (20 pts) The department chair will pay for 12 students to go to a conference. In how many ways can the 12 students be selected if exactly 3 are selected from each major