How many integer-valued solutions are there?
$$ x_1 + x_2 + x_3 + x_4 + x_5 = 63, x_i \ge 0, x_2 \le 9.$$
My Approach
$$ x_1 + x_2 + x_3 + x_4 + x_5 = 63, x_i \ge 0, x_2 \le 9.$$
$$ x_2' = x_2 - 9$$
$$ x_1 + x_2' + x_3 + x_4 + x_5 = 54, x_i \ge 0, x_2' \le 0 $$
... And I'm lost
... and "stalking" makes sense.
You do know that you can use "star and bars" to get the number of solutions for:
$$x_1+x_2+x_3+x_4+x_5=63,x_i\ge0,$$
and from this question you asked one hour ago you know how to do it for
$$x_1+x_2+x_3+x_4+x_5=63,x_i\ge 0,x_2\ge 10.,$$
Subtract the number and you will get the count for this question.