Suppose you have a bag with 11 balls in it, and you have placed 11 buckets on the floor (where each bucket has a label affixed to it; say, the buckets are labeled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11). Now, consider the following experiment. You draw a ball from the bag, toss the ball into one of the buckets, and record the bucket in which the ball landed (for simplicity, assume that the ball has to land in a bucket; i.e., you cannot “miss” all of the buckets and hit the floor, or anything like that). You repeat this procedure until your bag of balls is empty (at which point the experiment has concluded). Let S denote the sample space for this experiment, and define the events E and F as follows. E: All of the balls are in one bucket at the conclusion of the experiment. F: No bucket is empty at the conclusion of the experiment. (a) What is n(S)? Can S be viewed as a Cartesian product? Give an example of an outcome in S

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose you have a bag with 11 balls in it, and you have placed 11 buckets on the
floor (where each bucket has a label affixed to it; say, the buckets are labeled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11). Now, consider the following experiment. You draw a ball from the bag, toss the ball into one of the
buckets, and record the bucket in which the ball landed (for simplicity, assume that the ball has to land
in a bucket; i.e., you cannot “miss” all of the buckets and hit the floor, or anything like that). You repeat
this procedure until your bag of balls is empty (at which point the experiment has concluded).
Let S denote the sample space for this experiment, and define the events E and F as follows.
E: All of the balls are in one bucket at the conclusion of the experiment.
F: No bucket is empty at the conclusion of the experiment.
(a) What is n(S)? Can S be viewed as a Cartesian product? Give an example of an outcome in S

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