What is the probability that you roll 4 die and get a sum less than or equal to 5?
So far, I have come up with this:
$x_1 + x_2 + x_3 + x_4 \leqslant5 $
$x_1, x_2, x_3, x_4 \leqslant6 $
$x_1, x_2, x_3, x_4 \geqslant 1$
Now we typically find $y_1, y_2, y_3$ and $y_4$ to adjust the equation for the constraints but the fact that there are two of them is throwing me off.
$y_1 = x_1 - 0 = x_1$
$y_2 = x_1 -7 $
I'm having a hard time seeing how we can transfer both of the equations above to the same variable and add it to the main equation nicely in order to find the slack variable and use the stars and bars method to find the answer.
Do we simply do
$y_1 = x_1 - 7 $ and so on ?
I know that this is a simple problem but I was wondering if anybody could explain the general rule to me so that I can solve others with a larger sum involved.