# An SSN is a Social Security number. How many SSNs have digits that sum to 2? How many SSNs have digits that sum to 3? These are 9 digit numbers with 0-9.

An SSN is a Social Security number.
How many SSNs have digits that sum to 2? How many SSNs have digits that sum to 3?
These are 9 digit numbers with 0-9.
My attempt would be:
200000000, 110000000
Do this multiple times but Im assuming theres a much more simple way and I just cant figure it out.
Any ideas?
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Caylee Davenport
Step 1
SSNs are issued in the form $abc-de-fghi$ where de form a group number that is issued in weird order, but is is never zero, and fghi form a serial number in the range 0001 to 9999. Finally abc has traditionally been related to area codes, but can nowadays (after the "randomization" introduced on June 25, 2011) also take other values, but it still cannot be 000. Therefore there is no SSN with digit sum 2 and there are only few SSNs with digit sum 3: They must have one of 001, 010, 100 as area code, one of 01, 10 as group code and one of 0001, 0010, 0100, 1000 as serial number.
Step 2
That makes a total of $3\cdot 2\cdot 4=24$ solutions.
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Urijah Estes
Step 1
This is related to how many way you can partition a number. When digits sum to 2 then we can write:
$2=1+1=2+0$ and $3=2+1=1+1+1=3+0$.
Step 2
So the number of ways you can write for 2 is: $\left(\genfrac{}{}{0}{}{9}{2}\right)+\left(\genfrac{}{}{0}{}{9}{1}\right)$ and for 3:$2\left(\genfrac{}{}{0}{}{9}{2}\right)+\left(\genfrac{}{}{0}{}{9}{3}\right)+\left(\genfrac{}{}{0}{}{9}{1}\right)$