I have a combinatorics problem:
How many non-negative integer are there for $x_1+x_2+x_3+x_4+x_5=12$ where $x_1<x_2<x_3$
I tried to subtract the number of integers in which $x_1=x_2=x_3$ from the number of the whole possible solutions.However I could not do the rest.Can you enlighten me ,please?
Note: $x_1,x_2,x_3$ do not have to be consecutive. They are just smaller than each other ,respectively.