Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2: 62

Answer

Sample: "How many different 3-digit numbers can be written using digits 1, 2, 3, 4, 5, 6, 7, so that any chosen digit can appear only once ?"

Work Step by Step

The number of permutations possible if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. --------------- Sample answers: Example 1. How many differrent 3-letter words (a word is a 3-letter arrangement) using the letters A,B,C,D,E,F,G, so that each chosen letter appears once? Example 2. "How many different 3-digit numbers can be written using digits 1, 2, 3, 4, 5, 6, 7, so that any chosen digit can appear only once ?" Example 3. From a group of seven students, a president, vice-president, and secretary are to be chosen. In how many ways can this be done? Each sample problem involves selecting an ordered arrangement of 3 objects taken from 7, which leads to evaluating ${}_{7}P_{3}$,
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