You didn't specify whether the four digits must all be different
or not. I'll do it both ways.
If some of the digits can be the same:
choose the first digit 9 ways, <-- {1,2,3,4,5,6,7,8,9}
choose the second digit 10 ways, <-- {0,1,2,3,4,5,6,7,8,9}
choose the third digit 10 ways, <-- {0,1,2,3,4,5,6,7,8,9}
choose the fourth digit 5 ways, <-- {0,2,4,6,8}
That's 9∙10∙10∙5 = 4500 ways, if some digits can be the same.
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If the digits must all be different, there are two cases.
Case 1. 0 comes last
choose the fourth digit 1 ways, <-- {0}
choose the first digit 9 ways, <-- {1,2,3,4,5,6,7,8,9}
choose the second digit 8 ways, <-- not the same as 4th or 1st
choose the third digit 7 ways, <-- not the same as other three
That's 1∙9∙8∙7 = 504 ways for Case 1.
Case 2. 0 does not come last
choose the fourth digit 4 ways, <-- {2,4,6,8}
choose the first digit 8 ways, <-- not 0 and not the same as 4th
choose the second digit 8 ways, <-- not the same as 4th or 2nd
choose the third digit 7 ways, <-- not the same as 4th
That's 4∙8∙8∙7 = 1792
Total: 504+1792 = 2296 ways, if all digits must be different.
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[THING TO OBSERVE: ALWAYS CHOOSE THE MOST RESTRICTIVE THINGS
FIRST!!!]
Edwin
