$x_{i}$ = the face of the i dice, i=1,2,3,4
Determine the number of integer solutions of the equation
$x_{1}+x_{2}+x_{3}+x_{4}=14$
with the restriction
$1 \leq x_{i} \leq 6$
Converting the restriction, whe have:
$0 \leq x_{i}-1 \leq 5$
$x_{i}-1=y_{i}$
$x_{i}=y_{i}+1$
So, the new equation is
$y_{1}+y_{2}+y_{3}+y_{4}=10$
with the restriction
$y_{i} \leq 5$
But what do I do now? I know I have to use inclusion and exclusion, I was shown this formula below, but I don't understand what I have to do to find the values
$N=\left|S_1^c \cap S_2{ }^c \cap S_3^c \cap S_4^c\right|=|\Omega|-\left|S_1 \cup S_2 \cup S_3 \cup S_4\right|$