Answer
$
a-position\,6\\
b-position\,4\\
c-position\,1
$
Work Step by Step
$Hash(n)=n\,mod\,7=n-7(n\,div\,7)\\
a-\\
social\,number\,:
417-30-2072 \\
Hash(417302072)=417302072\,mod\,7=417302072-7(59,614,581)=5\\
but\,position\,5\,is\,occupied\,but\,position\,6\,is\,not\,\\
so\,add\,the\,social-number\,in\,position\,6 \\
b-\\
social\,number\,:
364-98-1703\\
Hash(364,981,703)=364,981,703\,mod\,7=364,981,703-7(52,140,243)=2\\
but\,position\,2\,is\,occupied\,(and\,3)\,but\,position\,4\,is\,not\,\\
so\,add\,the\,social-number\,in\,position\,4 \\
c-\\
social\,number\,:
283-09-0787\\
Hash(283,090,787)=283,090,787\,mod\,7=283,090,787-7(40,441,541)=0\\
but\,position\,0\,is\,occupied\,but\,position\,1\,is\,not\,\\
so\,add\,the\,social-number\,in\,position\,1 \\
$