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
logarithms, or even calculate an exact value using a computer program.)
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 Fall '11
 Wierman
 Probability, upper bound, standard deck, department chair, perfectly random order

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