1. (20 pts) Answer the following questions. Explain your reasoning where possible. Please note that the solution will not necessarily be a straightforward application of a counting rule that we studied in class: you may need to combine several rules. There are different ways of coming to the same correct answer for these questions. It may be helpful to visualize the system graphically or to discuss your reasoning with others in the class. a) (5 pts} How many ways can one arrange the six letters of the word SYSTEM? [Hint: the two letters "5\" are indistinguishable] b) (5 pts) How many ways can we make two teams of 5 players each out of a group of 10 people. Note that the two teams are indistinguishable and that the players on each team all play the same role c) (5 pts) Suppose that a room contains n people. What is the number of ways that at least two of them have a common birthday? For simplicity, assume that there are no leap years. [Hintz the answer will be an expression that is a function of n] d) (5 pts} A box contains 12 black and 8 green marbles. How many ways can 3 black and 2 green marbles be chosen