Calculate the number of even 3 digit positive integers with no repeated digits by finding the number of such integers that have:
1) unit digits 0
2) and non zero digits
Verify your answer by comparing the number of odd 3 digit postive integers with no repeated digits with the total number of 3 digit positive integers with no repeated digits

Question

Calculate the number of even 3 digit positive integers with no repeated digits by finding  the number of such integers that have:
1) unit digits 0
2) and non zero digits
Verify your answer by comparing the number of odd 3 digit postive integers with no repeated digits with the total number of 3 digit positive integers with no repeated digits

anonymous · Answer

1) ....-...-0
so (8)*9
2) ...-...-... 
     (8)*(9)*(9)
because (1)and(2) can never be at the same time  ! so the total is (9)*9*8+8*9
a number is odd if only  its unit digits is odd  
...-...-odd 
(8).(9).(5)
obviously 8*9*5<9*9*8+8*9