Combinations

Is it possible to evaluate C(9,12)? Explain.

Finance Math : Probability and Expected Value of a Payoff

Charles and Millie Jackson (a married couple in their 40’s) have decided to invest a portion of their accumulated retirement “nest-egg” in a new business venture. It is an opportunity that Millie found while exploring one of her hobbies. Her idea is to embroider logos for small companies and organizations. They have already priced the equipment to be a $10,000 investment, and after estimating variable costs, expect to make a profit of about $10 per shirt. Based on preliminary contacts, they believe there is a .30 probability (30 percent chance) that they could land a 3-year commitment from a local company, but only if they’ve made the investment and proven their product. This would lead... click for more

Exponential Generating Function for a Recurrence

Please see the attached file for the fully formatted problems.

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?