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Chapter 1: Q.1.3 (page 15)
Twenty workers are to be assigned to 20 different jobs, one to each job. How many different assignments are possible
The number of different possible assignments are
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Two experiments are to be performed. The first can result in any one of m possible outcomes. If the first experiment results in outcome i, then the second experiment can result in any of ni possible outcomes, i = 1, 2, ..., m. What is the number of possible outcomes of the two experiments?
Consider a group of people. If everyone shakes hands with everyone else, how many handshakes take place?
In how many ways can identical balls be distributed into urns so that the urn contains at least balls, for each ? Assume that .
Give an analytic proof of Equation (4.1).
From a group of people, suppose that we want to choose a committee of k, , one of whom is to be designated as chairperson.
(a) By focusing first on the choice of the committee and then on the choice of the chair, argue that there are role="math" localid="1647945358534" possible choices.
(b) By focusing first on the choice of the non-chair committee members and then on the choice of the chair, argue that there are role="math" localid="1647945372759" possible choices.
(c) By focusing first on the choice of the chair and then on the choice of the other committee members, argue that
there are role="math" localid="1647945385288" possible choices.
(d) Conclude from parts (a), (b), and (c) that role="math" localid="1647945400273" .
(e) Use the factorial definition of to verify the identity in part (d).
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