SOLUTION: How many different four-digit numbers can be formed from the digits 0 through 9 if the first digit must be even and cannot be zero?

Question 126821: How many different four-digit numbers can be formed from the digits 0 through 9 if the first digit must be even and cannot be zero?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Depends on whether you can repeat digits or not.

If you CAN repeat digits:

The first digit can only be 2, 4, 6, or 8, so there are 4 ways to pick the first digit.

Then there are 10 ways (0,1,2,3,4,5,6,7,8,9) to select each of the remaining 3 digits.

So the total number of 4 digit numbers under these conditions is:
4 X 10 X 10 X 10, or 4000.

On the other hand, if you are NOT allowed to repeat digits,

There are still the same 4 ways to select the first digit, but now there are only 9 ways to select the second digit because the selection for the first digit was eliminated from the selection pool. Likewise, there would only be 8 ways to select the 3rd digit and 7 ways to select the 4th and last digit.

So the total number of 4 digit numbers under these conditions is:
4 X 9 X 8 X 7 = 2016.
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