Find the number of submultisets of {$25 \cdot a, 25 \cdot b, 25 \cdot c, 25 \cdot d$} of size $80$.
I applied Inclusion-Exclusion to get; $$ {80+3\choose 3} - {4\choose1}\cdot{80-26+3\choose3} + {4\choose2}\cdot{80-2\cdot26 +3\choose 3}- {4\choose3}\cdot{80 - 3\cdot26 + 3 \choose 3}$$
Is this approach and answer correct?
The solution with the inclusion-exclusion principle is correct, but a bit long. A simple solution is about finding the number of non-negative solutions of $x+y+z+t = 100-80=20$. It is $$\dbinom{23}{3} = 1771 .$$