How many odd three-digit integers smaller than 500 are there such that all their digits are different?	Answers: A) 72 B) 88 C) 112 D) 122 E) 144
Case 1: Numbers starting with 1   1 _ _   The unit digit can take 4 numbers (3,5,7,9) to be ODD 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 2: Numbers starting with 2   2 _ _   The unit digit can take 5 numbers (1,3,5,7,9) to be ODD 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 3: Numbers starting with 3   3 _ _   The unit digit can take 4 numbers (1,5,7,9) to be ODD 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 4: Numbers starting with 4   4 _ _   The unit digit can take 5 numbers (1,3,5,7,9) to be ODD 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 32+40+32+40= 
<gadget id="calculator">32+40+32+40</gadget>
<output>144</output>
144, correct answer is 144
<result>E</result>
How many odd three-digit integers smaller than 500 are there such that all their digits are different?