Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:
a) 60,466,176.
b) 5,961,600.
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]
Item a:
No restrictions, hence for each of the five characters, there are 36 outcomes, hence [tex]n_1 = \cdots = n_5 = 36[/tex].
Then, the possible number of passwords is:
[tex]N = 36^5 = 60466176[/tex]
Item b:
The letters and the digits have to be alternated, hence:
Then, the possible number of passwords is:
[tex]N = 36^3 \times 10^2 + 10^3 \times 36^2 = 5961600[/tex]
To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866