Using the Fundamental Counting Theorem, it is found that the website would have 30,891,577,600 passwords.
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]
For this problem, the first six spaces of the password are letters, and each can assume 26 values, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 26[/tex]
The last two spaces are composed by digits, and each can assume 10 values, hence the parameters are:
[tex]n_7 = n_8 = 10[/tex]
Hence the number of possible passwords is given by:
N = 26^6 x 10² = 30,891,577,600.
The website would have 30,891,577,600 passwords.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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