How many five-digit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?
Select:
A) 36
B) 48
C) 72
D) 96
E) 144
Thus the last two digit must be 04, 12, 20, 24, 32, 40, or 52.   If the last two digits are 04, 20, or 40, the first three digits can take 4*3*2= 
<gadget id="calculator">4*3*2</gadget>
<output>24</output>
24 values.   Total for this case: 24*3= 
<gadget id="calculator">24*3</gadget>
<output>72</output>
72.   If the last two digits are 12, 24, 32, or 52, the first three digits can take 3*3*2= 
<gadget id="calculator">3*3*2</gadget>
<output>18</output>
18 values (that's because the first digit in this case cannot be 0, thus we are left only with 3 options for it not 4, as in previous case).   Total for this case: 18*4= 
<gadget id="calculator">18*4</gadget>
<output>72</output>
72.   Grand total 72 +72= 
<gadget id="calculator">72 +72</gadget>
<output>144</output>
144.   Answer: 144.
<result>E</result>
How many five-digit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?