fiona needs to choose a five - character pass...
fiona needs to choose a five - character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8. if she uses her initials, f, j, and s in order as the first three characters, and she does not use the same digit more than once in her password, how many different possible passwords are there? 10 20 24 40
Answer
# Explanation:
## Step1: Determine available digits
There are 5 even - numbers (0, 2, 4, 6, 8) and we need to fill 2 positions without repetition.
## Step2: Use permutation formula
The number of permutations of \(n\) objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 5\) and \(r=2\).
\[P(5,2)=\frac{5!}{(5 - 2)!}=\frac{5!}{3!}=\frac{5\times4\times3!}{3!}=20\]
# Answer:
20