If you generalize the solution of Exercise 1.7.2, you get the answer in the form Check that this is the same number as given in Theorem 1.7.1. Theorem 1.7.1 The number of ordered k-element subsets of a set with n elements is n(n − 1)···(n − k + 1). Exercise 1.7.2 Suppose that we record the order of all 100 athletes. (a) How many different outcomes can we have then? (b) How many of these give the same result for the first 10 places? (c) Show that the result above for the number of possible outcomes for the first 10 places can be also obtained using (a) and (b).

If you generalize the solution of Exercise 1.7.2, you get the answer in the form Check that this is the same number as given in Theorem 1.7.1. Theorem 1.7.1 The number of ordered k-element subsets of a set with n elements is n(n − 1)···(n − k + 1). Exercise 1.7.2 Suppose that we record the order of all 100 athletes. (a) How many different outcomes can we have then? (b) How many of these give the same result for the first 10 places? (c) Show that the result above for the number of possible outcomes for the first 10 places can be also obtained using (a) and (b).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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