This is my second question on MSE, as my first one had format issues. So apologies for that!
I have a problem here.
How many ways can you distribute 4 balls into 3 boxes?
I would calculate $x_1 + x_2 + x_3 = 4$ (right?) But further on, there is a fixed constraint on each of the variables, stating that only a maximum of $2$ is allowed in each box. (non negative allowed). So I write, $$y_1 = x_1 - 2, y_2 = x_2 - 2, y_3 = x_3 - 2$$
$$x_1 - 2 + x_2 -2 + x_3 -2 = 4-2-2-2$$ $$y_1+y_2+y_3 = -2$$
I am stuck there. It gives a negative value, how will I be able to count for it? Please correct me and help if there are any problems!
Thank you so much! :)