Correct Answer - Option 4 : 728
Concept:
Find the total number of thousand place, hundred places and unit digit.
Calculation:
In 4000 to 7000 , the thousand place digit are \(\in {4, 5,6}\)
Case 1: Thousand place digit is even, i.e., 4, 6
⇒ Then there are only \(\dfrac {4+5}{2}-1 = 4\) possibilities for the units digit.
This leaves 8 possible digits for the hundreds place and 7 for the tens places,
⇒ Total of even integers = 2. 8.7.4 = 448
Case 2: Thousand place digit is odd, i.e., 5
⇒ There are 5 choices for the units digit, with 8 digits for the hundreds and 7 for the tens place. This gives 1.8.7.5 = 280 possibilities.
The total number of even integers = 448 + 280 = 728