How many even 3 digit integers greater than 700 with distinct non zero digits are there ? Choose the correct choice from the following choices
A) 729  B) 243  C) 108  D) 88  E) 77
1. Number of 3 digit even numbers &gt;than 700 and &lt;1000 = 149. We can use Arithmetic progression to find 149. How? 702 is the first even number and 998 is the last even number. The difference is 2 between the numbers. So, we have 702 + (n-1)2 = 998 or n=149.   2. Number of 3 digit even numbers that need to eliminated = 41, How? 702, 704, 706, 708, 710 =&gt; 5 numbers x 3 (for 70x, 80x and 90x series)= 15. Also, 720, 730...790 - 8 numbers x 3 = 24. Also 800 and 900 - 2 numbers. So, 15 + 24 + 2 = 41.   3. So net result is 149-41= 
<gadget id="calculator">149-41</gadget>
<output>108</output>
108.   4. 108 is the answer.
<result>C</result>
How many even 3 digit integers greater than 700 with distinct non zero digits are there ?