- If $x_i\ge 0$ where $i \in\{1,2,3,4\}$
- If $x_1\ge 2$ ,$x_2 \ge 3$, $0 \le x_4 \le 2$
What I tried :
for the first question I subtracted the number of possible solutions of $x_1 + x_2 +x_3 +x_4 < 19$ from the number of possible solutions of $x_1 + x_2 +x_3 +x_4 <= 20$.
For the second I used the replacement: $y_1= x_1 - 2$, $y_2= x_2 -3$, $y_3=x_3$ , $y_4=x_3$ and I am searching for the number of ways to place $15$ balls in $4$ boxes where box $3$ takes up to $15$ balls and box $4$ up to $2$ balls. I don't know if it is correct ...