Thank you for reporting, we will resolve it shortly
Q.
The number of integers $x, y, z, w$ such that $x+y+z+w=20$ and $x, y, z, w \geq-1$, is
Permutations and Combinations
Solution:
Put $x=a-1, y=b-1, z=c-1, w=d-1$, then $a, b, c, d \geq 0$ and $(a-1)+(b-1)+(c-1)+(d-1)=20$ $\Rightarrow a+b+c+d=24$
The number of non-negative integral solutions of this equation is
${ }^{24+4-1} C_{4-1}={ }^{27} C_3$