Number of positive integral solutions to $x+y+z+w=20$ with $xWhat is the number of positive unequal integral solution of the equation $x+y+z+w=20$, if $\,x<y<z<w\,$ and $\,x,y,z,w\ge1\;?$ 
How to solve this question?

For a count of the solutions without restriction on the order by inclusion-exclusion, see this answer. The result is $552$; then the number of ordered solutions is obtained as $\frac{552}{4!}=23$.
