How many even 4-digit integers greater than 8000 are there such that all their digits are different?  Pick one:	A) 240	B) 369	C) 469	D) 520	E) 599
Case 1: Numbers starting with 8 followed by EVEN number   The hundreds digit can take 4 numbers (0,2,4,6) so 4 ways   The unit digit can take remaining 3 EVEN numbers left after using 2, to be EVEN so 3 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=4*3*7= 
<gadget id="calculator">4*3*7</gadget>
<output>84</output>
84   Case 2: Numbers starting with 8 followed by ODD number   The hundreds digit can take 5 numbers (1,3,5,7,9) so 5 ways   The unit digit can take remaining 4 EVEN numbers (0,2,4,6) to be EVEN so 4 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=5*4*7= 
<gadget id="calculator">5*4*7</gadget>
<output>140</output>
140   Case 3: Numbers starting with 9 followed by EVEN number   The hundreds digit can take 5 numbers (0,2,4,6,8) so 5 ways   The unit digit can take remaining 4 EVEN numbers left after using 1, to be EVEN so 3 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=5*3*7= 
<gadget id="calculator">5*3*7</gadget>
<output>105</output>
105   Case 4: Numbers starting with 9 followed by ODD number   The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways   The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.   The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways   Total=4*5*7= 
<gadget id="calculator">4*5*7</gadget>
<output>140</output>
140   Hence 84+140+105+140= 
<gadget id="calculator">84+140+105+140</gadget>
<output>469</output>
469, correct answer is 469
<result>C</result>
How many even 4-digit integers greater than 8000 are there such that all their digits are different?