Combinations and Permutations - password case

Question

Passwords on a network are made up of two parts. One part consists of three letters of the alphabet, not necessarily different, and five digits, not necessarily different. How many passwords are possible on this network?

Answer 1

I am going to assume that these passwords are not case sensitive. So there are 26 distinct letters and 10 distinct digits. I am also going to assume that the two "parts" you describe have fixed positions, e.g. the passwords are made up of 3 sequential letters followed by 5 sequential digits.

If my assumptions are true, then total number of possible passwords is $26^3 \cdot 10^5 = 1,757,600,000$.

Visually, consider each possible password character: _ _ _ _ _ _ _ _. Since characters are allowed to repeat, total number of possibilities is the product of the numbers of possibilities at each position, i.e. $26 \times 26 \times 26 \times 10 \times 10 \times 10 \times 10 \times 10$, i.e. $26^3\cdot 10^5$.