How many integer solutions exist for the following equation with the given constraint:
Equation: $X_1 + X_2 + X_3 + X_4 = N$
Constraint: $1 \le X_1 \lt X_2 \lt X_3 \lt X_4 \le N$
I went as far as the number of integer solutions without the constraint which is $C( 4+N-1 , N-1 )$. I thought about applying the inclusion-exclusion theorem but I couldn't go any further with that.