How many three-digit numbers are there such that all three digits are different and the first digit is not zero? Select: A) 504 B) 648 C) 720 D) 729 E) 810
The first digit cannot be 0, so there are 9 options for the first digit.   the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1) 9 possibilities for the 2nd digit.   The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2) 8 possibilities for the 3rd digit.   So there are  9 * 9 * 8= 
<gadget id="calculator"> 9 * 9 * 8</gadget>
<output>648</output>
648 possibilities.   ANSWER:648
<result>B</result>
How many three-digit numbers are there such that all three digits are different and the first digit is not zero?