f you add the digits in a #, how many #s between 0 and 10000 will have a sum of 10?

**help1** · October 18th 2007, 08:56 AM

"If you add the digits in a number, how many numbers between 0 and 10000 will have a sum of 10?"

Could you guys help me solve this, and please explain it to me? If I get it right, I will be able to get extra credit on my Math average!

**Plato** · October 18th 2007, 09:40 AM

Originally Posted by help1

"If you add the digits in a number, how many numbers between 0 and 10000 will have a sum of 10?"
Could you guys help me solve this, and please explain it to me? If I get it right, I will be able to get extra credit on my Math average!

Well at least your are honest!
So here is a suggestion. There are four places to put ten ones. How many ways can you put ten ones into four different places? But take away the cases where a place has more than nine ones.

Or you can find the coefficient of $x^{10}$ in the expansion of
$\left( {\sum\limits_{k = 0}^9 {x^k } } \right)^4$

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