#### 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 ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$.
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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 ${}_{7}P_{3}$,