On June 25, 2011, the Social Security Administration (SSA) made changes to the m

Question

On June 25, 2011, the Social Security Administration (SSA) made changes to the method and exclusion rules used for assigning Social Security Numbers (SSNs). With the changes, the computer's random number generator will draw numbers from a pool of allowed numbers that are still available (unassigned). The pool of allowed numbers (including numbers that are no longer available because they have already been assigned) is determined by the following specification: The first 3 digits is called the area number; theoretically, it can range from 000 through 999 (inclusive) but 000, 666, and any number from 900 through 999 (inclusive) are not to be used by rule. The next 2 digits is called the group number; theoretically, it can range from 00 through 99 (inclusive) but 00 is not to be used by rule. The last 4 digits is called the serial number; theoretically, it can range from 0000 through 9999 (inclusive) but 0000 is not to be used by rule. Based on the above specification, determine exactly how many (distinct) SSNs there are in the pool of allowed numbers.

Explanation / Answer

The first 3 digits:- 000 to 999 excl 000,666 and from 900 to 999 which means total of (1000-102=898)

The next two digits:- 00 to 99 excl 00 which means 98

The last four digits:- 0000 to 9999 excl 0000 which means 9998

Therefore, the total number of distinct SSNs would be 898*98*9998=879863992

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