Exponential Generating Function

I would like an explanation of how to do this type of problem. If you have recommendations for a good book or website on the subject I would find that helpful as well, but that's not required; mostly I just need to know how to solve this problem. See attached file for full problem description.

Calculate effective annual interest rate

You've worked out a line of credit arrangement that allows you borrow up to $70M at any time. The interest rate is .480% per month. In addition , 5% of the amount that you borrow must be deposited in a non interest-bearing account. Assume that your bank uses compound interest on its line of credit loans. 1) What is the effective annual interest rate on this lending arrangement? Answer should be: 6.23% 2) Suppose you need $15M today and you repay it in six months - How much interest will you pay? Answer: should be: 460,228.73

Latin Squares

1) Show that for n less than or equal to 4, any Latin square of order n can be obtained from the multiplication table of a group by permuting rows, columns, and symbols. Show that this is not true for n=5 2) If n is an order for which mutually orthogonal Latin squares exist, does every Latin square of order n have an orthogonal partner?

Combinations and Permutations

1) Identify each of the following 1) as a permutation or combination and 2) as with or without replacement: a) Social security numbers b) Books in your backpack c) Numbers chosen for the “Big” lotto d) The cards in your hand for a card game e) Lunch chosen by a student from the cafeteria menu 2) A cafeteria offers 4 main menu selections, 5 salad selections, 3 fruit selections and 8 drink selections. How many ways can a student choose a lunch if... f) The student chooses one of each of the selections? g) The student chooses two different main menu selections (must be different) and one salad? h) The student chooses 3 salads (different), and a fruit? ... click for more

Partition of a set

Prove that if a partition g is finer than a partition f, then any union of sets of f is a union of sets of g.