Question

Social Security numbers are of the formXYZ - MN - ABCD.The first three digits XYZ are referred toas the area number. The number isassociated with where you registered foryour social security card. X is a number 1- 7. Y and Z can be any number 0 – 9.Also the area code 666 has never beenused. The middle two digits MN arereferred to as the group number. Thegroup number can be any number from01 to 99 (it cannot be 00). The last 4 digitsABCD are the serial number. The serialnumber can be any from 0001 to 9999 (itcannot be 0000). Additionally, thenumber social security number 123-45-6789 is only used in advertisements. Howmany social security numbers arepossible?

Answer 1

For XYZ

`\begin{gathered} (7*10*10)\text{ = 700} \\ 700-1=699\text{ways} \\ \end{gathered}`

For MN

`\begin{gathered} (10*10)\text{ =100} \\ 100-1=99\text{ways} \end{gathered}`

For ABCD

`\begin{gathered} (10*10*10)\text{ =10,000} \\ 10,000-1\text{ =9,999ways} \end{gathered}`

Finally

`\begin{gathered} (699*99*9999)-1 \\ =691,940,798\text{ } \end{gathered}`

Social security numbers are

possible 691, 940,798