How many odd four-digit integers greater than 9000 are there such that all their digits are different?
Choose the correct choice.
A) 84
B) 104
C) 168
D) 224
E) 280
Case 1: Numbers starting with 9 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 4 numbers (1,3,5,7) to be ODD 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 9 followed by an ODD number   The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways   The unit digit can take remaining 3 ODD numbers left after using 2 ODD numbers 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   Hence 140+84= 
<gadget id="calculator">140+84</gadget>
<output>224</output>
224, correct answer is 224
<result>D</result>
How many odd four-digit integers greater than 9000 are there such that all their digits are different?