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