fiona needs to choose a five - character password with a combination of three letters and the even numbers…
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?\no 10\no 20\no 24\no 40
Answer
Explanation:
Step1: Analyze remaining characters
Since the first three characters are fixed as F, J, S, we need to find the number of ways to choose and arrange the last two - character which are digits. There are 5 even numbers (0, 2, 4, 6, 8) and we need to choose 2 of them without repetition.
Step2: Use permutation formula
The number of permutations of (n) objects taken (r) at a time is given by (P(n,r)=\frac{n!}{(n - r)!}). Here, (n = 5) (the 5 even numbers) and (r=2). [P(5,2)=\frac{5!}{(5 - 2)!}=\frac{5!}{3!}=\frac{5\times4\times3!}{3!}=5\times4 = 20]
Answer:
20