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Lecture2

# Lecture2 - Combinatorics You are eating at Emiles...

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Combinatorics You are eating at ´ Emile’s restaurant and the waiter informs you that you have 1. two choices for appetizers: soup or juice; 2. three for the main course: a meat, fish, or vegetable dish; and 3. two for dessert: ice cream or cake. How many possible choices do you have for your complete meal? 1

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ice cream cake ice cream cake ice cream cake ice cream cake ice cream cake ice cream cake (start) soup meat fish vegetable juice meat fish vegetable 2
Assume that the owner of ´ Emile’s restaurant has observed that 80 percent of his customers choose the soup for an appetizer and 20 percent choose juice. Of those who choose soup, 50 percent choose meat, 30 percent choose fish, and 20 percent choose the vegetable dish. Of those who choose juice for an appetizer, 30 percent choose meat, 40 percent choose fish, and 30 percent choose the vegetable dish. What is the probability that a customer eats vegetable. 3

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(start) soup meat fish vegetable juice .8 .2 .2 .3 .3 .4 .5 .3 meat fish vegetable ω (ω) ω ω ω ω ω ω .4 .24 .16 .06 .08 .06 m 1 2 3 4 5 6 4
Prove that at least two people in Atlanta, Georgia, have the same initials, assuming no one has more than four initials.

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