Question

There are 8 characters in a password. The password can have upper case, lower case, or one of 32 special characters. How many different passwords are possible. Why?

Answer 1

if you can repeat characters, any position can have one of \(26\times 26\times 32\) different characters. by the counting principle that means you have \(\left(26^2\times 32\right)^8\) possible combinations

Answer 2

that makes a lot of sense! thanks!
do you think you could help me with one more related problem?