How many 6-digit numbers can you make without using the same digit twice?
You can choose the 1st digit any of 9 ways 1,2,3,4,5,6,7,8,9. You can't
choose 0 for the first digit since it wouldn't be a 6-digit number.
That's 9 ways to choose the first digit.
For each of those 9 ways you can choose the 1st digit, there are 9 ways
you can choose the 2nd digit. You can't choose what you chose for the 1st
digit, but you can choose 0 for the 2nd digit, so that's 9*9 ways to choose
the first 2 digits.
For each of those 9*9 ways you can choose the 1st 2 digits, there are 8 ways
you can choose the 3rd digit. So that's 9*9*8 ways to choose the first
3 digits.
For each of those 9*9*8 ways you can choose the 1st 3 digits, there are 7 ways
you can choose the 4th digit. So that's 9*9*8*7 ways to choose the first
4 digits.
For each of those 9*9*8*7 ways you can choose the 1st 4 digits, there are 6 ways
you can choose the 5th digit. So that's 9*9*8*7*6 ways to choose the first
5 digits.
For each of those 9*9*8*7*6 ways you can choose the 1st 5 digits, there are 5
ways you can choose the 5th digit. So that's 9*9*8*7*6*5 ways to choose the
first 6 digits.
And that's all of them, so the anser is
9*9*8*7*6*5 or 136080 ways.
Edwin
