There are how many 4-digit even numbers if the first digit cannot be a zero? Choose the most appropriate option.
A) 3,600
B) 3,645
C) 4,500
D) 4,999
E) 5,000
FIRST, lets write down the restrictions   1) these are four digit even numbers, so first digit can be 1 to 9, and the units digit can be 2,4,6,8, or 0..   2) any number of repetition can be done..   Now, lets work out a solution on these restrictions   1) units digit= any of five even digits.. 0,2,4,6,8..   2) at tens and hundreds position any of the ten digits can be placed ..   3) at thousands place, any of the 10 except 0 can be placed...   the ways= 5*10*10*9= 
<gadget id="calculator">5*10*10*9</gadget>
<output>4_500</output>
4500   another way   1) what are the different ways without any restriction=10*10*10*10=10,000..   2) out of these ways in which first digit is 0...= 1*10*10*10=1000..   3) Remaining= 10000-1000= 
<gadget id="calculator">10000-1000</gadget>
<output>9_000</output>
9000   4) Half of 9000 will be even and other half odd.. so even= 9000/2=4500..   Ans 4,500
<result>C</result>
There are how many 4-digit even numbers if the first digit cannot be a zero?