Principle of inclusion-exclusion

2. Principle of Inclusion-Exclusion (18 points) (1) (2 points) Every student in a discrete mathematics class is either a com- puter science or a mathematics major or is a joint major in these two subjects. How many students are in the class if there are 38 computer science majors (including joint majors), 23 mathematics majors (includ- ing joint majors), and 7 joint majors? (2) (16 points) How many strings of eight uppercase English letters are there (a) if letters can be repeated? (b) if no letter can be repeated? (c) that start with X, if letters can be repeated? (d) that start with X, if no letter can be repeated? (e) that start and end with X, if letters can be repeated? (f) that start with the letters CS (in that order), if letters can be re- peated? (g) that start and end with the letters CS (in that order), if letters can be repeated