Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1105: 79


The main difference is that in a permutation, the order or sequence matters, while in a combination, the order does not matter.

Work Step by Step

We know that a permutation is an arrangement of items in order. It occurs when no item is used more than once, and also the arrangement of the order makes a difference. ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ And a combination of items occurs when the selection is made from the same group and no item is used more than one time; also, the order makes no difference. ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ Let us consider an example: if someone has to select 4 people from a group of 10. In this case, combination is used to determine the number of ways to select 4 people. Also, consider an example: if someone has to find a 5-letter password such that there is no repetition in the letters. Thus, in this case, a permutation is used as no letter is repeated.
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