Question

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 1

The first three characters are fixed as F, J, S. The last two must be distinct even digits from {0,2,4,6,8}, so there are 5 choices for the fourth character and then 4 remaining choices for the fifth: 5 × 4 = 20.

Answer: 20