How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 3, whithout any of the digits repeating?	Choose the correct answer.
A) 15 B) 96 C) 120 D) 181 E) 216
First step:   We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0,1,2,3,4,5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   {1, 2, 3, 4, 5} and {0, 1, 2, 4, 5}. How many 5 digit numbers can be formed using this two sets:   {1, 2, 3, 4, 5} --&gt; 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   {0, 1, 2, 4, 5} --&gt; here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --&gt; 5!-4!=96   120+96= 
<gadget id="calculator">120+96</gadget>
<output>216</output>
216   Answer: 216.
<result>E</result>
How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 3, whithout any of the digits repeating?