## Thinking Mathematically (6th Edition)

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 ${}_{7}P_{3}$,