Question 1045303: How many three-digit number are there with no dight reapeated?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! ONE WAY TO LOOK AT IT:
Taking  different digits, out of the  available,
we can make  different three-digit strings,
but the one starting with zero, such as  or  , cannot be considered three-digit numbers.
Among the  three-digit strings, there are a few that start with zero.
How many? As many as the number of two-digit strings we can make using the  non-zero digits,
 .
That leaves us with 
ANOTHER WAY TO LOOK AT IT:
When trying to write a three-digit number are there with no digit repeated,
you have choices for the hundreds digit, because you would not start with  .
After you choose your hundreds digit, there are  other, different digits left to choose your tens digit from.
After you have chosen the first  digits,
there are  other, different digits left to choose your units digit from.
All in all, you have  different three-digit number are there with no digit repeated.
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