How many even three-digit integers greater than 700 are there such that all their digits are different? Pick one:
A) 40 B) 72 C) 80 D) 112 E) 120
Case 1: Numbers starting with 7   7 _ _   The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total = 8*5= 
<gadget id="calculator">8*5</gadget>
<output>40</output>
40   Case 2: Numbers starting with 8   8 _ _   The unit digit can take 4 numbers (0,2,4,6) to be EVEN so 4 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total= 8*4= 
<gadget id="calculator">8*4</gadget>
<output>32</output>
32   Case 3: Numbers starting with 9   9 _ _   The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.   The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.   Total= 8 *5= 
<gadget id="calculator">8 *5</gadget>
<output>40</output>
40   Hence 40+32+40=72, correct answer is 112
<result>D</result>
How many even three-digit integers greater than 700 are there such that all their digits are different?