Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.6 Basics of Counting Theory - 11.6 Exercises - Page 1061: 36


(sample answer) When taking r distinct elements at a time from a set of n elements, if the order of selecting or presenting the r elements matters, we are talking about permutations. If the order is unimportant, we have combinations. Say that we are selecting from the set of n=10 digits. Examples of combinations problems: - choose 3 "lucky" digits - make a 4 element subset consisting of these digits. Examples of permutations problems - make a 4-digit passcode for your padlock, with no digits repeating. - select a PIN (personal ID) made of 5 digits, with no digits repeating. - write all arrangements using all the ten digits.

Work Step by Step

Note: the "no repetition" clause serves the purpose of selecting r distinct elements from the set of n elements.
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