Question 1026710
 
Question:
Jane wants to create a password for one of her Internet accounts using some portion of her street name, which is “soundview.”  If the password is restricted to 5 characters, how many different passwords can she create?    
 
Solution:
The word soundview has 9 distinct characters.
The number of ways 5 selected letters can be arranged is the permutation of 5 objects chosen out of 9, or
{{{P(9,5)=9!/(9-5)!}}}
=9*8*7*6*5
= 15120
Alternatively, for the first letter there are 9 choices, for the second letter,there are 8 choices...until the fifth letter, there are 5 choices.
So by the multiplication rule, there are 9*8*7*6*5 = 15120 passwords.