How many even four-digit integers smaller than 2000 are there such that all their digits are different?  Choices
A) 190	B) 212	C) 224	D) 240	E) 280
Case 1: Numbers starting with 1 followed by an 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 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 2: Numbers starting with 1 followed by an ODD number   The hundreds digit can take 4 numbers (3,5,7,9) 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 140+140= 
<gadget id="calculator">140+140</gadget>
<output>280</output>
280, correct answer is 280
<result>E</result>
How many even four-digit integers smaller than 2000 are there such that all their digits are different?