in Combinatory
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How many 5-digit even numbers have all digits distinct?

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Number of 5-digit even numbers with all distinct digits 

Case 1 : Fix 0 at one’s place and most significant digit can’t be 0 

So number of possibilities = 9 X 8 X 7 X 6 X1 = 3024

Case 2 : We can have {2,4,6,8} at one’s place(hence 4 possibility) and most significant digit can’t be 0

So number of possibilities = 8 X 8 X 7 X 6 X4 = 10752

Total =   13776

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