How many ways can a four digit number equals nineteen without repeating same four numbers

Question

I want to know all ways you can get sum 19 using four numbers without them repeating the same four numbers how many ar?

Answer 1

This is a very difficult combinatorics question. I started looking at it and it will probably take way too much time for somebody to solve and write up for you here. Check out these links I found for similar problems, there are multiple ways to solve this and you should be able to adapt their solutions to this problem. Just know that your problem is actually harder because 19 is a larger number than 12 and 17:

 

https://math.stackexchange.com/questions/153876/how-many-ways-can-the-sum-of-4-positive-integers-equal-12

https://www.quora.com/How-many-4-digit-numbers-are-there-with-the-Sum-of-digits-as-17