550.420 Introduction to Probability Fall 2011 Homework 1 Due Thursday September 8 1. (2 points) A salad bar has 3 choices of greens, 5 veggies, 4 fruits, 3 dairy items, and 4 dressings. In how many ways can I make myself a salad with at least two of the greens, 3 veggies, only one dairy item, no more than 2 fruits, and exactly one dressing? 2. (2 points) Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. The group is split in half at random. What is the probability that each half contains exactly N women and N men? Approximate your answer using Stirling’s Formula. 3. ( 3 points) Have the Cards Been Seen in This Order Before? [a] Give an expression (containing at most 4 symbols) for the number of possible orderings of a standard deck of 52 playing cards. Calculate an approximate numerical value for your expression, which you expect to be accurate to at least three significant digits. (You may use a Stirling’s formula approximation, an estimate by summing
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