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Fiona needs to chose 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

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For the five characters of the five-character password, the first three slots are already taken for the initial F, J, S, the password would become,
                                         FJS_ _
The last two slots could be any of the even digits. In the fourth slot, Fiona can have any of the 5 values. On the fifth slot, she can have only 4 choices as the other digit was already used. Multiplying 5 and 4, the answer would be 20. 

Using the Fundamental Counting Theorem, it is found that 20 different possible passwords are there.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

  • The first 3 characters are fixed, hence [tex]n_1 = n_2 = n_3 = 1[/tex].
  • The last 2 are non-repeating digits from a set of 5, hence [tex]n_4 = 5, n_5 = 4[/tex].

Then:

[tex]N = n_1n_2n_3n_4n_5 = 5(4) = 20[/tex]

20 different possible passwords are there.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866