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?

It's equivalent to solving $y+z+w=19$ which in turn is equivalent to selecting $19$ elements out of a set of $3$ elements where repetition is allowed.
The answer is thus ${n+k-1 \choose k}={21 \choose 3} = 1330$
