How do I solve this probability question?

Question

Consider a four character password, where each character can be an upper or lower case letter or

a digit. No character can be used more than once (no repeats).

1) How many different passwords are possible?

2) How many different passwords have the character "A" in them?

3) How many different passwords are possible if the first character must be a capital letter, the

third character must be a digit, and the fourth character must be lower case?

Answer 1

Total possible # of characters=26 + 26 (uppercase and lowercase letters + 10 (digits) or 62 characters

For the password, # possibilities is

62*61*60*59. The number of possible character choices decreases by one because no character can be reused.

# different passwords with the letter "A" is

1*61*60*59*(4!)/(1!*3!)

The letter "A" represents only 1 possible choice. 61, 60, and 59 represent the other possible choices. (4!)/(1!*3!) represents the possible arrangements where "A" could appear in the password. "A" could be the first, second, third, or fourth character to appear in the password.