We can pick the first digit in any of 6 ways,

For each of the 6 ways we can pick the first digit,
we can pick the second digit any of the same 6 ways.
So there are 6×6 or 36 ways to pick the first two digits.
 
For each of the 6×6 or 36 ways we can pick the first two digits,
we can pick the third digit any of the same 6 ways.
So there are 6×6×6 or 216 ways to pick the three digits.

Answer: 216

We can pick the first digit in any of 6 ways,

For each of the 6 ways we can pick the first digit,
we can only pick the second digit any of 5 ways, since we can't use the digit we
picked for the first digit.
So there are 6×5 or 30 ways to pick the first two digits.
 
For each of the 6×5 or 30 ways we can pick the first two digits,
we can only pick the third digit any of 4 ways, since we can't use either of the
two digits we picked for the first and second digits.
So there are 6×5×4 or 120 ways to pick the three digits.

Answer: 120

Edwin

1.  If repetition is allowed, the answer is  .


2.  If repetition is NOT allowed, the answer is  6*5*4.