How many social security numbers are available if the only restriction is that the number 000-00-0000 cannot be assigned?

Each digit can be 0-9 ( 10 numbers)
 there are 9 numbers in a social security number

multiply 10 nine times:
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =  1,000,000,000 ( 1 billion) possibilities.
 
 the restriction is it can't be all zeros so subtract 1 from the total
 1,000,000,000 - 1 = 999,999,999 combinations

It is better to use completing the square method to solve this quadratic equation.