Please help! The access code to a houses security system consists of 8 digits. How many different codes are available if each digit can NOT be repeated?

Consider one of eight positions separately from all others. There are 10 possible ways to choose
a digit to place on this position since there are ten digits from 0 to 9, and this choice is
independent of all other positions since each digit can be repeated and there is no restriction on
how to choose digits.
So, we have 8 positions and each one is filled by a digit in 10 ways independently from each other,
therefore the total number of possible codes equals to ways it can be done for each independent
position multiplied altogether. This is 10 × 10 × … × 10 = 108
(100 million).
108 different codes.