How many five-digit numbers are there who digits sum to 39?
Can someone give me their answer so I can check if mine is right? Thank you!
One expands $\displaystyle \left( {\sum\limits_{k = 1}^9 {x^k } } \right)\left( {\sum\limits_{k = 0}^9 {x^k } } \right)^4 $.
The coefficient of $\displaystyle x^{39}$ is the answer.
Notice the first sum starts at $\displaystyle k=1$ because the first digit in a five digit number cannot be zero.
Here is an online tool you can use.